I need to replace burned out Lead Wire Ceramic Fuse T3.15A 250V in my power supply station for robot vacuum by resettable fuse. What resettable fuse would you recommend?

 

I would not recommend other than the exact replacement fuse.
Check the label for the rated current, which should be less, and add a circuit breaker with a current rating just a bit above that value but below the 3.12 amp rating.