False Triggering of when Intergration of TI SE555 with Maxim MAX6866 IC
"Issue:- Whenever I turn on the Power , 555 got Trigger by somehow. "  You have designed the the 555 circuit to trigger on power up (R34,C42,R36). 

On power up C42 is discharged (0V across it) so it will pull the trigger input low to begin with. 

Simple solution - remove C42

A more reliable solution is to add a power up reset circuit (RC delay on pin 4) and use an edge trigger circuit at pin 2 so pin 2 is pulled up to 5V on power up.