Correct spelling, explanation: this word comes directly from Latin (also senior), meaning older. The word hasn’t been changed in any way in English, it is a direct loanword. Therefore seniour or any other change in spelling is incorrect. The only correct form is senior.

Definition of senior:
adjective, of a higher competence or older
He doesn’t have enough experience to become a senior manager.
noun, somebody older than another, usually in the family (father-son relation); in school: a student in their last year or final class
James is a senior in our family; James Jr is his son.

Incorrect spelling, explanation: seniour is a misspelling, probably made due to the fact, that -or in American English is often written as -our in British English. This word, senior, is however a Latin loanword, and it is spelled exactly like in Latin. Therefore senior is the only correct form.

Incorrect spelling

Incorrect spelling

Incorrect spelling