Competete a variant of Compete used in colloquial speech, but is written with the same spelling as the latter, has come into use (at the least) in Indian English variants if in no other English variants.
The question here is how could it have been formed? I had a few ideas of my own:
1) It is maybe the result of -tion deletion which generally adds a t sound in return, thus adding an extra t sound after compete.
2) It is maybe the pronunciation /kum-pe-ti-shun/ and not /kom-puh-ti-shun/ which requires the extra t sound syllable to maintain the pronunciation stress on pe - /kum-pe-teet/ and not /kum-peet/
Edit: this is unlike association -> associate and connotation -> connotate