Service kids forks 20” wheel
Most of these older design entry level fork have no serviceable parts the best you can do is disassembly it and cover all the moving parts in grease. On most this requires removal of the little plastic caps on the top. If you shine a flashlight in you will likely see a 5mm allen screw. To remove the screw you need a "LONG" allen wrench. Alternatively you can purchase a 3/8" drive 5mm socket and use a 3/8" drive socket extension to remove the screws. Count the number of turn it takes to remove the screw so they can be reinstalled in the same position.  Once the screws are removed the lowers will slide off. Clean everything on the lower inside and upper outsides. Examine the upper legs for rust and if necessary sand smooth and spray with epoxy paint. Cover everything with grease (I use white lithium) and reassemble. After all of this you may notice  little if any difference. Most of the forks I have seen on kids bikes are so stiff that children don't weigh enough to compress the fork anyway.