אַתֶּם חַייָבִים לְהַאֲמִין לִי, לֹא עָשִׂיתִי אֶת זֶה
זה גם מה שדודו טופז אמר.
זה גם מה שביל קלינטון אמר.
got is also correct
"got" is not also correct, but you must say in colloquial English" "you gotta believe me..."
On it's own got is wrong but not with have. "I've got to" is by far the most common way to express obligation or necessity.
I think that "I have to" is just as common as "I've got to."
I think what you meant to write is: "Another correct way to say this is, 'You've got to believe me...."
You've gotten six downvotes because your assertion was incomplete.