Can I connect 14 gauge wire to a light fixture that came with 16 gauge wire. This is for lighting in a outside shed.

Yes.. 14 gauge is heavier wire than 16 gauge is and you will not be creating a dangerous situation from undersized wire.

Almost all lighting and fans are factory wired with 16 or even 18 AWG. Should not be an issue.

Good question thou. I rather someone ask questions than assume.

Thanks for getting back to me with the answers. I feel better now knowing it will not be a potential hazard.