Recently, Alfvénic ion temperature gradient (AITG) modes have been observed in the core plasma on the HL-2A tokamak. Only when electron cyclotron resonance heating (ECRH) and neutral beam injection are simultaneously injected into the deuterium plasma do the AITG modes become unstable. The instability is electromagnetic and localised in the core plasma with an internal transport barrier. Dynamic evolution of AITG modes is greatly affected by the off-axis ECRH. Theoretical analysis suggests that there is a strong dependence of the AITG modes on $\eta _i\simeq \boldsymbol{\nabla }\ln T_i/\boldsymbol{\nabla }\ln n_i$, where $n_i$ is the ion density. It is also found that ECRH can enhances AITG modes by causing a drop of electron density and an increase of $\tau =T_e/T_i$; here $T_e$ and $T_i$ are the electron and ion temperatures, respectively. Besides, high-power ECRH may also change the safety factor or magnetic shear and then contribute to the mitigation of AITG modes. The new findings can not only enrich scientific knowledge for pressure gradient-driven instability, but also be beneficial to active control of core-localised electromagnetic modes in future fusion devices.