There was an episode where satyakAma jabala of unknown lineage was accepted as a disciple. Similarly, on the recent there happened another incident where King Prasenadi from the lineage of shAkhya was convinced by revered Gautam Buddha to accept his son as shAkhya only when the later was found to be conceived by woman of 4th class unknowingly. These two episodes are dealt in this article names The Buddha was every inch a Hindu
He predicted the coming of a future awakened leader like himself, the Maitreya (“the one practising friendship/charity”), and specified that he would be born in a Brahmin family. *When King Prasenadi discovered that his wife was not a Shakya princess but the daughter of the Shakya ruler by a maid-servant, he repudiated her and their son; but his friend the Buddha made him take them back.
Did he achieve this by saying that birth is unimportant, that “caste is bad” or that “caste doesn’t matter”, as the Ambedkarites claim? No, he reminded the king of the old view (then apparently in the process of being replaced with a stricter view) that caste was passed on exclusively in the paternal line. Among hybrids of horses and donkeys, the progeny of a horse stallion and a donkey mare whinnies, like its father, while the progeny of a donkey stallion and a horse mare brays, also like its father. So, in the oldest Upanishad, Satyakama Jabala is accepted by his Brahmin-only teacher because his father is deduced to be a Brahmin, regardless of his mother being a maid-servant. And similarly, King Prasenadi should accept his son as a Kshatriya, even though his mother was not a full-blooded Shakya Kshatriya.
So what this article is saying is progeny invariably derive its gotra from it's father lineage irrespective of the fact varNaSaMkara happened or not which was supported by Buddha.
Is this claim supported or deduced by scriptures? This question indirectly asking - what gotra to assign to the progeny born out of intermixing of classes?