The normal thing is to choose a combination of tool and tool holder that will work with your lathe. Without a picture or a clear statement about the type of tool holder that you have, it is hard to say what needs to be corrected.
Many tool holders have a way to adjust the height of the tool.
The old fashioned "lantern" style tool post with the tool in an Armstrong style holder is almost infinitely adjustable.
lantern tool post - Bing
But if you had that I doubt that you would be asking this question.
Quick Change tool posts also have adjustments for the height. It is possible that you have one but it is too large for your lathe and the adjustment is out of range.
quick change tool post - Bing
The height adjustment is on the individual tool holders in the form of a thumb nut on a vertical screw in this example. This allows each tool to be adjusted individually for the best result.
I suspect that you have some form of a simple,
turret style tool holder.
lathe tool post - Bing
These do not normally have any height adjustment. The tool holder and the tool size are BOTH selected to bring the top of the tool below the center line of the lathe. Then the tool is shimmed up to bring it on center. Actual, physical shims must be used.
I suggest that you look closely for any height adjustment on your present tool holder. If there really isn't one, then you have a bad combination. You need to change either the tool bit size (12mm?) or the size of the holder or both.
Also look under the tool holder to see if it has been shimmed up. If there is a removable shim there, take it out and see haw things are.
This sounds like a used lathe and some tooling was included with the deal. Many used machines are sold by people who do not understand them and, due to that ignorance, the tooling you got may have been ill matched to it.
PS: If you wish to upgrade to a better tool post and want to make your own, you may want to consider my design. It is somewhat easier to make because you do not have to cut any dovetails. It can be sized for your lathe and has all the adjustments. There isn't a faster Quick Change Tool Post anywhere.
Quick Change Tool Post for Lathe - HomemadeTools.net