Why a specific temperature for value of 1 calorie?
why temperature such as 0 or 1 degree celsius is not chosen??

That has been chosen by some.
According to Physical Laboratory Experiments: Part III.--Heat, 4th edition (1912) :

The following different calories should not be confused:

ZERO DEGREE CALORIE:- The quantity of heat required to raise one gram of water from 0 [degrees] C to 1 [degree] C.

ORDINARY CALORIE: cal.-The quantity of heat required to raise one gram of water from 15 [degrees] C to 16 [degree] C, this being taken as the mean room temperature.

MEAN CALORIE OR ICE CALORIMETER CALORIE: The one-hundred part of heat required to raise one gram of water from 0 [degrees] C to 100 [degrees] C.

...



Heat capacity of liquid water is a continuously varying function of temperature itself, so a particular temperature or temperature interval must be specified.  Various intervals were chosen historically, and when a small interval near 15 degrees C is chosen it is because that was thought of as room temperature 100-200 years ago.