hi
I need to design score broad
I need to switch 12V 7 segment display using micro controller
My supply voltage also 12V
Display takes 350mA when its all segments are lit.
so I need to confirm my design will work or Any suggestion circuit
attachment is my design

 

That switching arrangement looks ok.

 

The common pin no need to connect to +V, because the pin was designed for the parts as relay or motor or some inductive parts.

If the c output of Q2 need 350 mA then the base must be providing 35mA, I'm afraid your circuit can't offer the heavy current.
I like to use the driver as below, it's quite normal.