Let V & E denote the gravitational potential and gravitational field at a point it is possible to have

V denote gravitational potential

E denote gravitational field

Then it is possible to have

i) $\text{V}=\text{0,}\text{E = 0}$  

when we consider an unit mass from a given mass M at a distance $\text{r}\to \propto$

then we can have

$\text{V}=\frac{-\text{GM}}{\text{r}}$

$\text{E}=\frac{-\text{GM}}{{\text{r}}^2}$

ii) $\text{V}=\text{0 \&}\text{E }\ne \text{ 0}$

it is not possible

(iii) $\text{V}\ne 0,\text{E}=0$  is possible in the case of hollow spherical shell we get V

at centre is not zero but E = 0

(iv) $\text{V}\ne 0\text{and}\text{E}\ne 0$  is always possible in many illustrations