if we calculate the field between two point on a wire taking the same value of ΔV (as of battery)

You cannot choose to take the potential between two points of a wire. It can be however be calculated if one knows the resistance and the current flowing through the two points. So if a current $i$ passes through the wire and the two points under consideration have distance $l$ with resistance between them as $R_l$ then the potential difference between the points is $iR_l$. If $\rho$ is the resistivity and $A$ is the cross-sectional area then $$R_l=\frac{\rho l}A$$ and consequently the electric field between the points is $$E=\frac{iR_l}{l}=\frac{i\rho}A=constant$$

Edit: As mentioned by @jensen paull resistance does not determine poteential difference. I wrongly stated that it did and I fixed it in my edit.

if we calculate the field between two point on a wire taking the same value of ΔV (as of battery)

You cannot choose to take the potential between two points of a wire. It can be however be calculated if one knows the resistance and the current flowing through the two points. So if a current $i$ passes through the wire and the two points under consideration have distance $l$ with resistance between them as $R_l$ then the potential difference between the points is $iR_l$. If $\rho$ is the resistivity and $A$ is the cross-sectional area then $$R_l=\frac{\rho l}A$$ and consequently the electric field between the points is $$E=\frac{iR_l}{l}=\frac{i\rho}A=constant$$

Edit: As mentioned by @jensen paull resistance does not determine potential difference. I wrongly stated that it did and I fixed it in my edit.

if we calculate the field between two point on a wire taking the same value of ΔV (as of battery)

You cannot choose to take the potential between two points of a wire. It is determined by the resistance of the wire. So if a current $i$ passes through the wire and the two points under consideration have distance $l$ with resistance between them as $R_l$ then the potential difference between the points is $iR_l$. If $\rho$ is the resistivity and $A$ is the cross-sectional area then $$R_l=\frac{\rho l}A$$ and consequently the electric field between the points is $$E=\frac{iR_l}{l}=\frac{i\rho}A=constant$$

if we calculate the field between two point on a wire taking the same value of ΔV (as of battery)

You cannot choose to take the potential between two points of a wire. It can be however be calculated if one knows the resistance and the current flowing through the two points. So if a current $i$ passes through the wire and the two points under consideration have distance $l$ with resistance between them as $R_l$ then the potential difference between the points is $iR_l$. If $\rho$ is the resistivity and $A$ is the cross-sectional area then $$R_l=\frac{\rho l}A$$ and consequently the electric field between the points is $$E=\frac{iR_l}{l}=\frac{i\rho}A=constant$$

Edit: As mentioned by @jensen paull resistance does not determine poteential difference. I wrongly stated that it did and I fixed it in my edit.