Is the word quickly a contraction word?

No, the word quickly is an adverb, a word that modifies a verb; for example:

He ran quickly to catch the bus.

We quickly finished our chores so we could go to the movie.

A contraction is two words shortened into one, placing an apostrophe where letters are removed and the two words joined, for example:

I am = I'm

you have = you've

that is = that's

would have = would've

they are = they're