Hello,
I'm a non-US citizen at a US medical school currently in my 4th year and I'm in the interview season for residency right now.
The ability of residency programs to sponsor visas varies between institution and also between specialty, so while hospital X may provide J1/H1B for medicine, they may not provide for surgery. (What specialty are you thinking of) It is mostly random, but I found that often state schools such as the UC schools, UW schools, etc were less likely to sponsor H1B's than programs associated with private universities. There was no "list" per say that I found. What I did was look on the website of each of the residency programs I was interested in, to see if they mentioned H1B. The best bet is to check the "application process" or "FAQ" section of the program. Usually they will say something like this:
"We support H1B for international students" - good to go
"We support H1B for non-citizens at US med schools but only J1 for students at international schools" - good to go
"We only provide J1 for graduates of international medical schools" -> This is ambiguous, so call the program coordinator and explain you're a non-US citizen at a US med school and looking for H1B
"We do not support H1B"
Some programs don't offer any info at all, so call the program coordinator and explain your situation.
Other things you could do, is ask upper years at your med school who are internationals applying in the same specialty, or ask the person who "runs" the international student program at your school, usually one of the deans, for more info.
When you actually fill out the ERAS application, there's a box for citizenship status, and if you put non-US citizen, a box opens up where you put your visa status (like F1) and then another box opens up, about whether you want to apply for H1B, J1, both, or neither. I checked the H1B box only. I got interviews at programs that I wasn't sure if they sponsored or not, since I could not reach their program coordinator. I assume they saw that I checked the H1b, or else they wasted both my time and theirs by interviewing me. Which is also a possibility.
I assume (and have heard from admissions/counsellors/people) that they will take the H1B requirement into consideration when ranking me (It will probably hurt my chances, I'm not sure though) and then come March, I would match, and I would then start the H1b paperwork process with the program that matched me.
