In an online employment questionnaire, I was asked to state my highest degree qualification. The selections were: PhD, postdoc, bachelor, master etc. I completed my PhD 3 years ago and I just finished my postdoctoral research fellowship.

My question is: should I state my highest qualification as postdoc? Though I know postdoc is not a qualification, it is a job. I am just wondering if i state my qualification as postdoc, I might have a higher chance to get the job.

Postdoc should fall under work experience not under qualification.

Well if it says postdoc there and you've done a postdoc, then select postdoc? They won't award you a prize for being pedantic.