Saving bank account - H1B

[sthomas14]

Hello All,

I'm on my H1B. I'm looking to deposit my money on a savings account that builds up. I inquired some banks and they got back to me saying that I wasn't eligible as I'm not a green card holder or a citizen. I have been living in the US from 2011. Can you please suggest me a bank that I can use to deposit money on a savings account with H1B visa, please. I really appreciate the help. Good day :

[abecede]

Have you tried wells fargo? That was my first for checking&savings. I assume you've already tried the bank you use for your paycheck?