Hello, I am working in family business since 2016 now want to appear for cat. will it be considered? its fulltime and paid.

Hi,
As long as you hold a specific role in the company, you can present this as valid work experience. I believe that you might need proof of appointment or salary slips or a certificate of experience issued from your firm evidencing your role there. [It is also important to note that the company needs to be a legally registered entity]. I hope this helps!

Its registered as a sole proprietorship firm. Will it be considered?

Yes, you need to show the proof of employment and stuff and it should be considered under work experience is what I believe.