Removing ink from leather is not a cleaning problem.
Ink is a dye and has re-coloured the leather (this is what it is meant to do).
Most ink removal products will not work simply because of the length of time the ink has been on the leather.

The longer the ink has been on the leather the harder it is to remove because it soaks into the finish. Once it has soaked into the finish you have to use very strong products to remove it, which will also remove finish and pigment which then need replacing.

Pigmented/Protected leather
If the ink is on a pigmented leather then the first thing you should try is an Ink lifter Stick. The fresher the ink the more chance you have of removing it. It is a good idea to have one in your house if you have pale leather and children!
Old ink will be harder to remove than new ink and may mean resorting to solvents which will also remove the finish. This is probably best left to the experts.
If an ink stick doesn't work a solvent based remover will need to be used and it may also remove finish and pigment so is best left to the experts.
Regularly using a good quality protection cream on your leather acts like a 'scotchgard' and will make any more mishaps easier to clean off.
You will see many people recommending household products to remove ink – this is not recommended as most simply will not work. Some may appear to work but the damage they cause can make a much bigger problem which is then un-repairable (even by a technician).

Do NOT  use the following:
Hairspray - This is very risky as it can make the matter far worse by spreading the ink over a bigger area and can sometimes then be impossible to fix.
Nail varnish remover/solvents will remove the finish on the leather even if you cannot tell it is doing so and this will then need replacing, and alcohol may do the same depending on the strength of the finish on the leather.
Baby wipes – just about the worst thing you can use on leather as they break down the finish and will eventually ruin it.
Milk or toothpaste - these will leave sticky residues on the surface which will help to break down the finish on your leather.
Silicones/furniture polish – should not be used on leather. They will form a coating on the surface of the leather which will not allow any moisture to get to the leather itself and will eventually break all the finish down and cause it to crack.
Hide food will not remove ink and will leave residues on the leather which will attract dirt and oils.
Most leather cleaners will not remove ink unless a very good leather protector has been used on a regular basis.

Aniline Style Leather (a.k.a. Natural/Naked Leather)
As aniline style leathers are largely absorbent it means that the ink will have soaked straight into the leather itself.
This makes it impossible to remove. No product will successfully remove the ink.
DO NOT try ink removing products on aniline style leathers as most will leave a greasy residue which will then cause another problem.
Because aniline style leathers are absorbent the ink will carry on moving through the leather and may become less obvious over time. Cleaning and protecting will also help to dissipate the ink.