Those are water sprouts and should be cut back to the branch where they sprouted. https://extension.arizona.edu/sites/extension.arizona.edu/files/pubs/az1455.pdf

Strawberries need a lot more water than kumquats, so I don't know how accurate that information is.

I had a kumquat in a pot at our previous house. I had it in a pot that was HUGE, probably 24" across, and deeper then that. It thrived there. You're probably OK for now, but it will definitely need to be repotted next year. Don't forget to fertilize with the proper fertilizer at least once a month or you won't get any fruit.

And, yes, cut off those water sprouts. At this stage trim your tree for form... what you want it to be as it grows bigger.

lgteacher, thank you for providing that link. I will cut back the sprouts.

CA Kate, thank you. I will repot the kumquat next year. Have to decide what the right container is. Been reading about that; some say go for clay and some say plastic is best.

Fertilizing, yes. I've been using SuperThrive on all my plants.

No need to totally remove vigorous 'water sprouts' unless they grow awkwardly rubbing on another branch. It is a waste of the energy the plant has put in producing them. Just prune them to an eye. They will branch out and become good strong 'regular sprouts' flowering next season Even if you leave them intact they will branch out eventually.

Just make sure they are not rootstock suckers.

Actually,when I put on reading glasses and enlarged the pic. The leaves look like trifoliate. Does anybody else see that? I may be wrong.

They might be. That's why I warned about rootstock suckers in my post above.

What Steve said.

Steve, I have a rootstock suckers just starting to grow. I want to let it grow and do a cutting so I could use it at rootstock. Is it not a good idear? Thanks

I rooted mine when they were about 4 inches and 4 0ut of 5 rooted. Go for it.

Thank you Steve!

There were indeed rootstock suckers, three of them with very large needles - one was about 3 inches long. I clipped them off and will continue to monitor for rootstock suckers.

When I see rootstock suckers, I see opportunities for future grafts/practice and FREE trees.

These are my trifoliate suckers that I am trying to root after cutting them off from my kumquat trees (grafted onto standard and semi-dwarf rootstock).

I always have bad luck in rooting. I do use rooting hormone (Bonide), but I'm beginning to think it's a gimmick and there aren't enough hormone (IBA) is the powder to help. I need the stronger stuff or the one the university labs buy at their special scientific store instead of HD.

If any of them root, they will be upgraded to separate one gallon pots. I got a few citrus varieties I am itching to graft onto these.