I've been offered a "weekly allowance" he's asking for my bank login to do mobile check deposits. I know it's probably a scam but i created a completely new bank account. I know my information is on there but is it any safer? Can he still pull information like my social from the account?
You obviously thought this was a scam enough to open a new bank account. There are laws referred to as KYC (Know Your Customer) where financial institutions need to verify the identities of their customers so that money laundering and terrorist financing can be identified. Scammers, like your daddy, get around the KYC laws by running their money laundering operations through the accounts of people like you; so it's your account, authenticated with your credentials and your name on all the fraudulent transactions from which you will profit a little in the form of your "weekly allowance." But you knew this was a scam, that's why you opened the fresh account. Maybe in the future just don't participate in scams at all.