He worked so hard that he may get a pay raise.
Is the sentence correct? Should I use "might" instead of "may" here?
The sentence may be read in two different ways.
He worked so hard [in order] that he might get a pay raise.
If you are trying to imply the purpose he had when working hard, you must use “might” to reflect that was a past purpose.
He worked so hard that [as a result] he may get a pay raise
If you are trying to imply future possibility, you must use “may.”
It is not correct to assume that only one tense of a modal verb is correct for any meaning. One tense may grammatically imply one idea, and the other tense may grammatically imply a different idea.