Viswanath,
There might be some capacitors or a very small trimmer around the crystal, try to check the tolerances or change the capacitors.
2 min in 24h is too much. May be you get some other cheap 32768 crystals on ebay and check which one works better.
Oh, the trimmer should be 2-20pF max, If you have a frequency counter check the frequency as a counter and see if you are bad
within 1 min, that is 32768 Hz x 60= 1966080 periods. Check it out with a high impedance probe. If you calculate the 2 min/24h fail down to
1 sec actually you will have 32735 Hz instead. Pls check that also. Lower frequency normally shows a bigger capacity drift.
This is also an issue of older crystal wrist watches which I try tor repair if possible.
Also, please check the specification of the DS1307: ###Accuracy > 2 minutes/month at 25 C ###... (
https://www.futurlec.com/Dallas/DS1307.shtml)
Just a simple output on pin X1 an X2, without capacitor to trim the frequency.
Lets see how it works, good speed!
Thomas