More can be written -- more has been written -- but you might like to start with these:

• 'Were all people from the Roman Empire considered "Romans", or just people from the city of Rome?' by /u/QuickSpore
• this by /u/MarcusDohrelius
• "How did one prove Roman citizenship? Did this process change from ca. 500BCE to 212CE?" with linked replies by /u/ScipioAsina and LegalAction, and in this thread by Astrogator

And an April Fool's answer by Daeres

This is not to discourage discussion. More questions, data and debate are welcome.