It's a pattern. "intention" in such sentences* is usually followed by "of" +"-ing". It is not followed by "to" + infinitive. I have no intention of giving up.
I have no intention to give up.
We had every intention of leaving.
We have every intention to leave.
* Note that in other sentences, "intention" can be followed by "to" + infinitive. For example, "His intention was to broker peace". However, note the pattern difference.
Thank you very much.
However, I don't see any difference or any difference in the pattern and the meaning, I don't see any reason actually. Do you mean if I use the words I/you/ he/she etc. / have/has the intention the . . . -ing form has to follow?