Charges Q1 and Q2 lie inside and outside respectively of a closed Gaussian surface S.  Let E be the field at any point on S and ϕ be the flux of E over S:

Gauss's Law : ϕ=qenclosedε0E→ depends upon both Q1​ and Q2​ but ϕ depends only on  the charge enclosed by that surface (i.e. Q1).If Q1​ changes, both E and ϕ will change.If Q2​ changes, then E will change and ϕ remains same.If Q1=0​, ϕ is zero and E is non zero.