I know variants exist which exclude, "who walk not according to the he flesh, but according to the spirit". I understand the TR includes those words, but I am also aware of newly discovered witnesses which predate witnesses like Codex Sianiticus and Vaticanus, which do actually agree with MT. Mark 9:29 as an example is supported in P45, which is nearly a century older than the previously mentioned Codex. I haven't been able to find a treatise on Romans 8:1 though.
A good internet source for quick summaries of the textual situation is the NET bible which here reads:
The earliest and best witnesses of the Alexandrian and Western texts, as well as a few others (א* B D* F G 6 1506 1739 1881 pc co), have no additional words for v. 1. Later scribes (A D1 Ψ 81 365 629 pc vg) added the words μὴ κατὰ σάρκα περιπατοῦσιν (mh kata sarka peripatousin, “who do not walk according to the flesh”), while even later ones (א2 D2 33vid Ï) added ἀλλὰ κατὰ πνεῦμα (alla kata pneuma, “but [who do walk] according to the Spirit”). Both the external evidence and the internal evidence are compelling for the shortest reading. The scribes were evidently motivated to add such qualifications (interpolated from v. 4) to insulate Paul’s gospel from charges that it was characterized too much by grace. The KJV follows the longest reading found in Ï.
You can find similar details here as well.
א* means the original text of Sinaiticus (while 2א indicates that a corrector later changed the text of Sanaiticus) and B means the original text of Vaticanus. Any prior text would be a papyrus and so would be indicated by a lower-case p with a subscript indicating which papyrus. So if you look at Romans 5:17 you can see what p46 reads. For Romans 8:1 there's no reading given for p46. In fact, as the wikipedia page for p46 indicates, that manuscript is missing Rom 6:14–8:15.
In fact none of the early papyri contain this passage (you can verify that here, but also if any of them did have this passage they would be listed at the NET bible and at the list of textual variants). Sinaiticus and Vaticanus are the earliest sources with this verse.