In the early period of Christianity,   what proportion of Christians
were converted Jews. How well represented were converted Jews among
the Martyrs and   leaders of Christianity?

Assuming that Christinity was initially a Jewish sect, then pretty
well all the early converts would have been Jews.

For one thing, there would probably have been a language problem in
recruiting others during the early years.

So, my guess is 99.999%

I cannot imagine who else would have converted.

I'm not sure that 1st century Jews would have necessarily considered
themselves converts to a separate religion.  They may have simply seen
themselves, still, as Jews that accepted Jesus as the Jewish Messiah.

That may be neither here nor there in terms of your question, but I
just thought I'd mention it all the same.

Cheers,

pafalafa-ga

I think that there were quite a few non-Jews that converted.  In the
Bible this is directly mentioned:  the speaking in tongues at
Pentacost, when all listeners heard them speaking in their own
language (probably not literally*, but maybe the idea was that
non-Jews were hearing/understanding the apostles' message); the Roman
centurion; discussion of whether converts must be circumcised**; and
other things that I can't recall at the moment.
Also, the fact that Paul was persecuted and eventually killed by the
Romans, suggests that he was not just appealing to Jews.

*Greek and Latin were spoken in Palestine, almost certainly to some extent by Paul.
**I believe that the decision was that they did not have to
circumcised, suggesting that becoming a Christian was not joining a
recognized Jewish sect, but maybe someone will correct me on this.