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The Isobaric Multiplet Mass Equation (IMME) has been successful at predicting the masses of isobaric analogue states in the same multiplet, while its coefficients are known to follow trends as functions of mass number. The Atomic Mass Evaluation 2016 [Chin. Phys. C 41, 030003 (2017)] $^{44}$V mass value results in an negative $c$ coefficient for the IMME quadratic term. The $b$ and $c$ coefficients can provide constraints for construction of the isospin-nonconserving (INC) Hamiltonians for the $pf$ shell. The excitation energy of the $0^+, T=2$ level in $^{44}$V is currently unknown and can be used to constrain the $^{44}$Cr mass. The aim of the experiment was to perform high-precision mass measurements to resolve the difference between $^{44}$V isomeric and ground states, to test the IMME, and to provide ingredients for identifying the $0^+$, $T=2$ state in $^{44}$V. High-precision Penning trap mass spectrometry was performed at LEBIT, to measure the cyclotron frequency ratios of [$^{44g,m}$VO]$^+$ versus [$^{32}$SCO]$^+$, a reference mass, to extract both the isomeric and ground state masses of $^{44}$V. The mass excess of the ground and isomeric states in $^{44}$V were measured to be $-23\ 804.9(80)$ keV/$\text{c}^2$ and $-23\ 537.0(55)$ keV/$\text{c}^2$. This yielded a new proton separation energy of $S_p$ = 1\ 773(10) keV. The new mass values of $^{44}$V have been used to deduce the IMME $b$ and $c$ coefficients of the lowest $2^+$ and $6^+$ triplets in $A=44$. The $2^+$ $c$ coefficient is verified with the IMME trend and agrees with the shell-model predictions using charge-dependent Hamiltonians. The mirror energy differences were determined between $^{44}$V and $^{44}$Sc, in line with isospin-symmetry. The new value of the proton separation energy determined will be important for the determination of the $0^+$, $T=2$ state in $^{44}$V and for prediction of the mass of $^{44}$Cr.