I want to gain some skills by contributing to an existing/a promising open source project and also increase productive use of my time.
Do you have a suggestion ?
We can't know what interests you. Have a rummage through Github or one of the alternatives till you find a project (or even several) that will fit your 'itch'.
What skills have you got? Have you joined the community on Slack or mailing list for something that you are interested in? Have you attended a meetup in your city?
have you tried something like https://www.codetriage.com ?
You could do a TypeScript change I've been meaning to do for a while now on an open source repo I use:
https://github.com/sourcegraph/sourcegraph
The change: When viewing a file, the copy icon should put the file's path in clipboard instead of the window's url.