Note: I am only sharing what i’ve come across during my reading so in no way is this an extensive research that discusses all the theories. This article is only for informational purposes to contribute to English information on this book. So this article is not to convince anyone, as this book is already popularly rejected as an authoritative source.
What is this book?
Fiqh al-Riḍā sometimes also referred to as Fiqh al-Raḍawī is a book consisting of words attributed to Imam ʿAlī b. Mūsā al-Riḍā عليه السلام (d. 203 AH) the 8th Imam, what makes this book unique on the other hand is that it is believed by some to literally have been authored by the Imam in his own handwriting, hence there is no chain of narrators for anything at all; not for the original manuscript itself nor for the separate sayings collected in the book. Others suggested it was instead dictated by the Imam to someone, and the majority have rejected the attribution of this book to the Imam completely. There are several other theories, in this article we will not mention all of them.
The origin of the book
For hundreds of years this book was unknown, our classical scholars such as Shaykh al-Kulaynī (d. 329 AH), Shaykh al-Ṣaduq (d. 381 AH), Shaykh al-Mufīd (d. 413 AH) have never mentioned this book. Notably even the greatest authorities on ‘ilm al-Rijal from our classical scholars, like Shaykh al-Ṭūsī (d. 460 AH) and Shaykh al-Najāshī (d. ~463 AH), have never mentioned such book to even exist as it is not mentioned in their biographical works.
The first time this book appeared was with Mullah Taqī al-Majlisī (d. 1070 AH), his son Allamah Bāqir al-Majlisī (d. 1110 AH) explains how it reached him as follows:
وكتاب الفقه الرضا عليه السلام أخبرني به السيد الفاضل المحدث القاضي أمير حسين – طاب ثراه – بعد ما ورد أصفهان، قال. قد اتفق في بعض سني مجاورتي بيت الله الحرام، أن أتاني جماعة من أهل قم حاجين، وكان معهم كتاب قديم يوافق تاريخه عصر الرضا صلوات الله عليه، وسمعت الوالد – رحمه الله – أنه قال. سمعت السيد يقول. كان عليه خطه صلوات الله عليه، وكان عليه إجازات جماعة كثيرة من الفضلاء وقال السيد. حصل لي العلم بتلك القرائن أنه تأليف الإمام عليه السلام فأخذت الكتاب وكتبته وصححته، فأخذ والدي – قدس الله روحه – هذا الكتاب من السيد واستنسخه وصححه، وأكثر عباراته موافق لما يذكره الصدوق أبو جعفر بن بابويه في كتاب من لا يحضره الفقيه من غير سند، وما يذكره والده في رسالته إليه، وكثير من الأحكام التي ذكرها أصحابنا ولا يعلم مستندها مذكورة فيه
I was informed about the book Fiqh al-Riḍā (a.s.) by al-Sayyid, the virtuous traditionalist, the judge, Ameer Husayn (may Allah be Gracious to his soil) after returning to Isfahan. He said to me: ‘It happened that during the time when I was neighbouring the Sacred House of Allah, a group of the residents of Qum visited me while performing their hajj and they had with them an old book the date of its writing agreed with the date during which al-Riḍā, the blessings of Allah be upon him, was alive.
And I heard my father (rah) [Taqi al-Majlisi] saying: I heard al-Sayyid saying: it had his (a.s.) [the Imam] handwriting, and this was testified by many of the dignitaries, and the Sayyid [Husayn] said, “based on these indicators I have gained knowledge that this was the writing of the Imam (a.s.) so I took the book and wrote it down and corrected it”, so my father (qr) took this book from al-Sayyid [Husayn] and he copied it and corrected it, and most of its words is in accordance with what al-Ṣaduq Abū Jaʿfar b. Bābawayh has mentioned in his book ‘Man lā yaḥḍuruh al-faqīh without any chain of narrators, and what his father had mentioned in his letter to him, and our companions have mentioned many rulings without mentioning their chain of authorities which were mentioned in this bookBihar al-Anwar, vol 1, pg 11
Many questions arise;
For centuries this book was unknown, to our classical scholars and even the muta’akhireen, so for centuries there was not even a word about the existence of it, how is this possible?
How was Sayyid Husayn able to know it is the handwriting of the Imam when between him and the Imam is more than 800 years?
Who are these people from Qom who brought him this book? Are they reliable? How did they get this book?
It is mentioned many of its narrations can be found in books of Shaykh al-Ṣaduq; who is to say that the person who wrote Fiqh al-Riḍā didn’t take them from his books rather than the other way around? Especially since Shaykh al-Ṣaduq never mentioned the existence of this book either, not in his ʿUyūn akhbār al-Riḍā [which is a book with narrations from Imam al-Riḍā عليه السلام] nor in any other book.
Some indicators point to the possibility of this book being Kitab al-Takleef by Muhammad b. Ali al-Shalmaghani (d. 323 AH) also known as Ibn Abi ‘Azaqir. He was a contemporary of Abu al-Qāsim al-Ḥusayn b. Rūḥ al-Nawbakhtī (d. 326 AH), the 3rd deputy of the Mahdi (ajtf). He was one of the great scholars in his time but his envy towards al-Ḥusayn b. Rūḥ made him deviate, the fact that he wasn’t chosen as deputy contributed to this. 
Shaykh al-Najāshī mentions about him:
محمد بن علي الشلمغاني أبو جعفر المعروف بابن أبي العزاقر، كان متقدما في أصحابنا، فحمله الحسد لأبي القاسم الحسين بن روح على ترك المذهب والدخول في المذاهب الرديئة
Muhammad b. Ali al-Shalmaghani Abu Ja’far knowns as Ibn Abi al-‘Azaqir, he was one of our foremost companions, but then he carried envy towards Abi al-Qāsim al-Ḥusayn b. Rūḥ and left the madhab and entered the inferior madhahib […]Rijal al-Najashi, pg 378
Shaykh al-Ṭūsī mentions:
محمد بن علي الشلمغاني، يعرف بابن أبي العزاقر، غال.
Muhammad b. Ali al-Shalmaghani, known as Ibn Abi al-‘Azaqir, he became of the ghulat [exaggerators]Rijal al-Tusi, pg 448
In another place he says:
محمد بن علي الشلمغاني، يكنى أبا جعفر، ويعرف بابن أبي العزاقر، له كتب وروايات، وكان مستقيم الطريقة، ثم تغير وظهرت منه مقالات منكرة، إلى أن اخذه السلطان، فقتله وصلبه ببغداد.
وله من الكتب التي عملها في حال الاستقامة كتاب التكليف، أخبرنا به جماعة، عن أبي جعفر ابن بابويه، عن أبيه عنه، الا حديثا واحدا منه في باب الشهادات، انه يجوز للرجل ان يشهد لأخيه إذا كان له شاهد واحد من غير علم
Muhammad b. Ali al-Shalmaghani, named as Aba Ja’far, also known as Ibn Abi al-‘Azaqir, he has books and narrations, he was on the straight path, later on he changed and reprehensible words emerged from him, till the sultan took him, killed him and crucified him in Baghdad. And from the books which he authored in his time of uprightness, Kitab al-Takleef, a group of people narrated it to me, from Abi Ja’far b. Babawayh, from his father, from him [al-Shalmaghani], [the book was narrated to me] except for 1 hadith in the chapter of testimonies, [the hadith stated] that it is permissible for a man to testify for his brother if he has only 1 witness [even] without having knowledge [of the matter he is testifying for]Al-Fehrest, pg 224
And the hadith that is mentioned here as originally being part of Kitab al-Takleef, is still included in the book Fiqh al-Riḍā that we have today:
إذا كان لأخيك المؤمن على رجل حق، فدفعه عنه ولم يكن له من البينة إلا واحدة وكان الشاهد ثقة فسألته عن شهادته، فإذا أقامها عندك شهدت معه عند الحاكم على مثال ما شهد، لئلا يتوي حق امرئ مسلم
When your faithful brother has a right over another man, and he [the man] denies this right, and your brother does not have witnesses against him, except one person and he is a reliable witness, you turn to the witness and ask him about his testimonial. When he testifies to you, you testify along with him to the judge according to his testimony, so the right of a Muslim man is not trespassed.Fiqh al-Ridha, pg 308
In a different place Shaykh al-Ṭūsī references Shaykh al-Ṣaduq regarding the above narration:
واللفظ لابن بابويه وقال، هذا كذب منه ولسنا نعرف ذلك.
وقال: في موضع آخر كذب فيه
The word is from Ibn Bābawayh. He said: “This is a lie he has made and we don’t know of any such narration.”Kitab al-Ghayba (al-Tusi), pg 430
In another occasion he says, “He has lied.”
There are several narrations in the book that also have a problematic content, we will only quote one here that I could find commentary for:
In the chapter describing actions related to prayer, during the beginning of your salat:
واجعل واحدا من الأئمة نصب عينيك
And place one of the Imams before your eyes.Fiqh al-Ridha, pg 105
Shaykh Baqir Sharif al-Qurashi in his biography of Imam al-Riḍā عليه السلام says:
[..] the book contains some traditions which contradict the Shi‘ite beliefs such as extremism which the pure Imams disproved and regarded as infidels those who believe in it. For example, it has been mentioned in the book, Chapter on Istiqbal al-Qibla fi al-Salat: “And place one of the Imams before your eyes.” This is grievous extremism, for it is incumbent upon every worshipper to direct his sentiments and feelings towards Allah, the Creator of the universe and Giver of life. [..]The life of Imam ‘Ali Bin Musa al-Ridha
Allamah Majlisī also comments on this sentence: 
لم يذكر ذلك في خبر آخر
It is not mentioned in any other reportBihar al-Anwar, vol 81, pg 217