There really isn’t ever a reason to have a static bitcoin address, as @Murch mentioned in the comments, doing so has very real downsides, and no real upside.
That said, your wallet will (and should) present you with a new address for each and every payment you receive, however, any past address your wallet has presented to you will continue to work to receive funds in the future.
In other words, if you open your wallet and copy down the address, but then open/close your wallet 100 times (and get presented with 100 different addresses in the process), that won’t change anything about the validity of that original address. You can still receive funds to it, it is still a part of your wallet. Any good wallet will eventually contain a large collection of addresses!
I’m trying to get something deposited into my bank account and they have the wallet address but they want me to verify that it’s a static…
I’m curious who the ‘they’ is in this. Its hard to say without more information, but odd requests like this are sometimes the hallmarks of a scammer.