Pet breeding laws vary from state to state and even between different cities, but there are some general types of pets that can be kept, as well as some animals that are considered prohibited. Here's an overview:

Pets that are generally allowed to be raised:
dogs
Most states allow the breeding of dogs, but there are laws regarding certain breeds.
cats
Cats are very common as pets and there are usually no restrictions on keeping them.
hamsters
Small and easy animals to raise.
Rabbits
Common as pets and can be raised in foster homes.
parrots
Different types of parrots, such as conyora parrots or naga parrots, can be pets.
reptiles
Like snakes, lizards and turtles, there are species that can be kept as pets, depending on local laws.

Pets that may be prohibited or restricted:
wildlife
Breeding wild animals such as lions, tigers and bears is illegal in most places.
Certain breeds of dogs
In some countries there are restrictions on the breeding of certain breeds that are safer (like pit bulls).
Disease-carrying animals
Certain animals that may carry diseases or be dangerous to people or other animals may be prohibited.
exotic animals
Some exotic animals may require special licenses or be prohibited for breeding.

conclusion:
To determine which pets are allowed or not allowed in your area, it is recommended to check local laws, consult with local authorities or veterinarians.