Can you quit your job during the probation period?

If you have another offer, you can choose to burn the bridge and hop over. The consequences will then be having a "bad" record for the company that you are working at. They probably cant do much about it, but do take note that Singapore is not a very big country and for some fields, you are bound to see the same faces again. Do consider if it is worth it to do so (like better salary and progression), or you think the culture is a big mismatch, then try explain to them nicely and leave amicably.

I'm assuming your concern is more on how this impacts your career prospects?

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Take a step back and understand what a probation period is. It is a time for you and the company to work for work together and decide if this is the right fit for both parties.

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Your choice to quit during probation is thus just a decision that this is not the right fit for me.

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There are no consequences per se from quitting during probation, but how you quit, what you do after quitting, whether it was amicable or not, or if you burnt bridges are more likely what holds more consequence.