Which one is correct?
1) I have the intention to emigrate. OR
I have intention to emigrate. OR
I have an intention to emigrate.
2) "I am a supportman" OR "I am a supportsman"
For your first question, "the intention" is correct. The second question you asked was a little confusing. Did you mean a "sportsman" (someone who is active in sports)? Neither "supportman" nor "supportsman" are words. I hope this helps!