The Correct spelling is: compete
Common misspellings of the word compete are:
How do you spell compete?. It is not
intr.v., -petÂ·ed, -petÂ·ing, -petes.
To strive against another or others to attain a goal, such as an advantage or a victory. See synonyms at rival.
[Late Latin competere, to strive together, from Latin, to coincide, be suitable : com-, com- + petere, to seek.]