Will the power supply change the output in a Amplifier circuit?
Your power supply voltage will not affect the gain of the amplifier, but it will affect the voltage swing for the amplifier output. An opamp cannot output beyond its rails, and many opamps cannot approach the rails - see the opamp's specification for output voltage swing for details.

Since you're deriving the 5v offset from the power supply, you will need to adjust those resistors to give 1/3 of 15V instead of 1/4 of 20V.