I breastfeed my 2 month old baby only on demand.will this reduce my milk supply.do i need to keep a feeding schedule?

Milk supply is maintained by utilization. Schedules are good to push an increase until the milk is in but then you let baby control the system. There will likely be days they feed more or less often as growth often comes in spurts. Spurts push more frequent feeds. Feeding for more than ten minutes/side decreases recovery time & adds only a trickle of feed.

By 2 months, your milk supply should be good and feeding on demand is appropriate and should not decrease the supply. Your baby likely has somewhat of a schedule while feeding on demand. Once you're ready to wean your baby, do it gradually (if you can) so that the supply at the times you're still breastfeeding continues to be good.