jemaasjr is right about the question.
In US grammar school, we used to run through the tenses:
present tense - I stay, do stay, am staying.
We rarely use "I do stay" in this exact form, but it's absolutely essential for questions and negative statements.
Do you often stay up late?
Don't stay up too late!
past tense - I stayed, did stay, was staying
(The second one is defined as the past tense of "to do" plus the bare infinitive.)
Did you stay for the end of the game?
I didn't stay to see the fireworks.