One of the certificates you must get in order to work most carpentry jobs is the OSHA 10 (Occupational Safety and Hazard Awareness). It’s an easy course to take, mainly just going over what to be aware of in order to work safely.
Otherwise, you don’t need certificates to work in carpentry. Unless you want to work in a specialized field within carpentry, then you can take classes that focus on the skills you want to learn.
Beyond certificates, all you really need to make it in the carpentry world is a good work ethic, cleanliness and experience (which grows slowly but strongly over a long time). Enjoy the work! I know I do!
Isaac recommends the following next steps: