Can I replace a mail breaker in a Blakeman Brothers main panel with a quad breaker of a modern manufacturer?
And what type breaker will work?

Breakers must be UL Listed to be installed in panels, and vice versa.

I have never heard of this brand, not that means they do not exist, however, I cannot find any reference or photos of these breakers or panels. Cannot find anyone that sells surplus parts.

While a breaker may fit in a certain panel, it may not be legally allowed in that panel.

Can you post some photos of what you have?