Can I use some kind of adaptor to connect my Xbox one to wifi?

no you cannot it's already built into the system. If you're having connection issues you need to talk to your Internet provider

Ok let me rephrase then can I connect to internet via some adaptor since I can't wirelessly do it?

"I can use wifi whene I'm plugged into the router but I can't have it plugged into the router all the time."

If you're "plugged" into the router with an ethernet cable you can't use WiFi unless you disconnect the ethernet cable from the console.

Well no as it's not a pc

However xbox one has an built-in WiFi adapter like other current gen console

It's only ever happened playing Crucible for me.

I get disconnected waiting to respawn then I can no longer connect using wifi. It doesn't accept the password.

I've since been playing using wifi bridge instead of the built in wifi adaptor and now it never disconnects.

There is some kind of problem with the x1's built in wifi adaptor