Correct spelling


Correct spelling, explanation: entered is the correct spelling because it is a past form of the verb enter. Since enter is a regular verb, both past forms will look the same, with a -ed ending, hence entered. Entred is incorrect; a mistake made probably due to pronunciation, which may be misleading for some.

Definition of entered:
verb, past simple and past participle form of enter; to go in, to get inside; also: to type/put in
He entered the room, looked at me, and left. That was weird.
Have you entered the correct password? Maybe try again.

Incorrect spelling


Incorrect spelling, explanation: this form is incorrect because entered is a past form from the regular verb enter. Therefore -ed ending is added and the rest of the word isn’t changed (there are no orthographic reasons for changing anything else). Entred is incorrect and entered is the correct form.