Are you replacing an old Broan NuTone 696 b bathroom ventilation fan?
You'll need to buy part number C350BNR from Home Depot ($20 at the time of this writing). It's not much quieter than your original fan, but it'll fit and you won't have to re-cut the hole in your ceiling. It's also advertised as a 696N, but it'll be fine. Make sure that the slot for the power plug is on the side and not on the corner. There's a different 696 Broan-NuTone solution with the plug on the corner which won't fit. You need the one with the plug hole on the side.
There are no new/fancy replacement options for this type of fan housing that I could find. I wanted a quieter or fancier vent (some turn on the vent when humidity spikes, some have bluetooth, some have lights built in). This one is just a plastic fan replacement which is 95% as loud as the metal-fan-blade version that you're probably throwing in the trash, but at least you'll have a working fan.
Good luck!