Bicycle Mechanics - Rear derailleur not indexing properly

Can anyone give advice on my problem? I have a installed a shimano deore 9 speed derailleur, I changed the cable, set up the gears, but when it gets to 4th and 5th gear it hesitates, but if i fine tune it, then the higher gears struggle to go in.
Any suggestions?

What shifters? What cassette? provided the shift cables aren't sticking and everything is routed smoothly, it sounds like there's a mismatch between shifter # and cog #.

Even though the manufacturers like to say "9 speed derailleur", it means nothing: derailleurs don't care how many cogs you have on your cassette, they simply respond to what the shifter tells them to do.

All modern derailleurs can shift basically anything you want. For example, I use a "9 speed derailleur" but with a 7 speed cassette and 7 speed shifters.

Make sure your cable's clean and lubricated.

Make sure your housings are the correct length to minimise bends.

To ensure your housings are fully bedded in, shift to a small cog then shift back without pedalling; as the chain stops the derailleur you can crush all the slop out of your housings.

If you still have issues, try a fresh cable, or even fresh housings. You can also try adding tension to the derailleur's return spring (some derailleurs have an adjustment cam, but most will require some creative tweaking). Cranking up the return spring by enough gives great results.

The shifter is a Sachs Power grip plus, It is 8 speed, the cassette is 11 to 44 tooth, don't know make.

I would check the chain wear too. 12 links should be 12 inches.