Bicycle Mechanics - Finicky 9 speed

I went out for a ride this afternoon and early on had issues with my shifters. The set up is Ultegra 6500. The issue is the chain jumping from an intended lower cog to the next higher gear. It only occurs on the 6th,5th and 4th largest cog in combination with the small front chain ring. Sound like an adjustment issue? Not sure which way to go with the adjuster. Thanks in advance. Lp

There is less than 100 miles on this drive train. Lp

you may have a bend dérailleur hanger. Take the biek to a shop and they will have the tool to check

Turn the adjusting barrel at the back of the rear derailleur counterclockwise one-half turn and see if this reduces or solves the problem. Turn it further in one-half turn increments as needed until the bike shifts properly.

What you are experiencing is common with new cables as they bed in and "stretch" slightly with initial use.

Rear derailler barrel adjuster, turn to the right 1/4 turn at a time.

BEFORE adjusting any barrels, put the bike on a stand or have a friend hold up the rear wheel. shift the rear all the way to the smallest cog. while slowly pedaling, push the derailler cage in and let it come back on its own. This checks that the derailler moves freely on its own, independent of the cable. then, lube the bottom bracket cable guide, and make sure the cable guide is firmly fixed to the bike frame without play. then remove the rear wheel, push the derailler cage in to its limit, which will slacken the shift cable. check to make sure the cable slides smoothly thru the bottom bracket guide. if all this checks out ok, then adjust "cable tension" as has been correctly suggested. But:
does this happen under hard pedaling, or normal, light shifting?

BEFORE adjusting any barrels, put the bike on a stand or have a friend hold up the rear wheel. shift the rear all the way to the smallest cog. while slowly pedaling, push the derailler cage in and let it come back on its own. This checks that the derailler moves freely on its own, independent of the cable. then, lube the bottom bracket cable guide, and make sure the cable guide is firmly fixed to the bike frame without play. then remove the rear wheel, push the derailler cage in to its limit, which will slacken the shift cable. check to make sure the cable slides smoothly thru the bottom bracket guide. if all this checks out ok, then adjust "cable tension" as has been correctly suggested. But:
does this happen under hard pedaling, or normal, light shifting?
Pretty much all of these checks are to assure the cable moves freely. In the OP's case the cable is apparently moving too far and, thus, has to be moving freely. The inability to stay in a lower (bigger) cog says the cable is slightly too long or too slack.