Using a single power source for both the gate and source of my transistor?
Assuming R1 is a load you want to switch, you need to fix the circuit and choose a mosfet that will switch at 3.7V (or less).  The IRF44Z is not even characterized for Vgs of less than 4.5V and will have very significant Rds at Vgs of 3.7V.







simulate this circuit &ndash; Schematic created using CircuitLab