All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It isn`t permissible for a Muslim to use zero balance credit card while aware that doing so entails paying interest.
It is also impermissible to repay that debt in installments or to reschedule it while knowing that doing so entails paying interest, regardless of calling it (Service allowance) or (Interest).
In addition, charging what is called (Service allowance) isn`t permissible unless it was equal to the actual service presented by the bank and this requires the latter to use a certain policy to calculate the actual cost of issuing and using the card, but, unfortunately, this is practiced by a handful of Islamic banks.
As for non-Islamic banks, they impose this (Service allowance) on basis of forbidden (Interest). However, calling interest by another name doesn`t make it lawful. This is supported by the Hadith in which the Messenger of Allah (PBUH) said: "People among my Ummah (Nation) will drink Khamr (Intoxicants), calling it by another name." {Related by Abu Dawoud}. And Allah the Almighty knows best.