Your boyfriend may claim your shared son as a dependent if your son lives in the home with your boyfriend (his father) more than half the nights of the year, and if your boyfriend's taxable income is more than yours.
Your boyfriend may claim you as a dependent if you lived in his home the entire year, AND you have less than $4300 of taxable income, AND your boyfriend paid more than half your total support. Support your boyfriend paid includes 1/3 of rent, utilities, food and other household expenses, plus your expenses for medical, travel, entertainment, and so on. Government support is not provided by the boyfriend, so it is possible that your boyfriend does not pay more than half your total support once everything is calculated (Medicaid, food stamp, etc) but you would have to add everything up.
It is important to understand that if you qualify to be claimed as a dependent, you must answer "yes, I can be claimed as a dependent" even if you don't want to be claimed. For 2020, this means you won't get a stimulus payment in your own name. But if you filed a return and answered "no, I can't be claimed as a dependent" when you really could be, just to get the stimulus, that would be tax fraud.
Whether you can be claimed as a dependent is based on simple facts; where you live, how much you earn, and who supports you. It is not a moral judgement or approval of your situation. If you don't like your living situation, there are many options you might want to consider to change them, and many places where you can get help to move out of a bad situation. But it's not a tax problem.
