Will drinking Quinine water have any effect on your liver ?

No,

It should not affect you liver

For future reference my friend:

Side Effects of Quinine Water

Side Effect: Skin Rashes
Though side effects from quinine water are unusual, people who are sensitive to quinine should avoid it, Side effects of quinine include itching of the skin and rashes.

Side Effects: Bleeding
A serious side effect of quinine is a blood dyscrasia or abnormality called thrombocytopenia. Thrombocytopenia is a decreased number of the platelets responsible for blood clotting. This can cause significant bruising and bleeding.

Side Effect: Cardiac
Cardiac side effects of quinine include chest pain, irregular heartbeat, rapid heart rate and faintness.

Side Effect : Allergic Reaction
A serious side effect of quinine is severe allergic reaction. Although rare, quinine can cause swelling of the mouth, face and throat, respiratory distress and seizure.

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Contact your Doctor if you experience any of the side effects on this list.

I hope this information helps, just in case it is always good to be well informed.

Take care... from a caring individual