Resistivity of iron under pressure (p < 17 GPa) has been measured in a new type of Bridgman cell adapted to trap Daphne oil as pressure medium. Here we have done detailed studies on the T-exponent of ρ(T) in the low p-region of the superconducting phase (13 ≤ p ≤ 31 GPa) under magnetic field ( ≤ 8 kOe). Very large drop and quasi-complete ρ(T) transition were observed for the first time in the low-p region of SC-dome. With the increase of magnetic field we obtained, below TSC onset, a trend that the T-exponent is increasing and reached to 1.82 at the highest applied field. Attempt has also been made to estimate the critical current density, which appears to be quite high compared to our earlier work.