Some banks are starting to offer OAuth access to accounts for use by Mint and other like tools. Bank of America and Chase are examples.
That said I don’t if it’s possible to use as an individual or small developer. My guess is not really. But I don’t know for sure.
I do know that You Need A Budget offers an API that’s well documented and can be used by any customer. So you could sign up for YNAB, have it pull data from your bank account, and then use the YNAB API to access your data. This is very roundabout but it would work.
Good luck.