Tribal lineage if adopted and converted?

So, as a Jew who was born to a Jewish mother and a Catholic father- I have no tribe, but what happens to those adopted by Jews who are formally converted? Do they somehow inherit their adopted father’s tribe, or are they tribeless like me?

I’m asking because I read an article today about Sharia Law, and the issues Muslims have with adoption, and it occurred to me that I have no idea what we do with adoption as it pertains to the tribe issue.