A few correct options (changes italic):
- After I retire, I want to be a happy person. [The verb retire requires a subject. Unlike some languages, English usually allows an implied pronoun subject only in commands.]
- In retirement, I want to be a happy person. [This one sounds a little unidiomatic to me, but it's correct. Retirement is the state of being retired; "after retirement" would be when you are no longer retired (e.g., you have started working again).]
- When [or "Once"] I am retired, I want to be a happy person. [See below for explanation. This wording could be interpreted as you being forced into retirement.]
- After retiring, I want to be a happy person. [Correct as it stands, but some people might interpret it using another meaning of retire, which is "to go to bed."]
I searched in internet, it seems "After retired" is a correct expression because retired can be an adj.
Retired is an adjective, as you noted, but the construction you are using requires an adverb modifying the main verb. In the meaning you were using, after is a preposition and requires a noun or equivalent (a noun clause, in my edited version) as an object. I would use when or once in this case because they are less likely to be interpreted as forced retirement than "After I am retired" is. (Strictly, "After I am retired" either means someone is retiring you or means that you are no longer retired.)