The study aims at assigning a bijective mapping ς that maps the vertices of a graph G to its own cardinality whose corresponding edge weights are defined by the sum of its end vertices such that it satisfies certain coloring conditions. A graph G is deemed to possess an equitable local edge antimagic coloring, that corresponds to the minimum number of colors if it meets both equitable edge and local edge antimagic coloring conditions. Ascertaining the equitable local edge antimagic connection number of any graph is considered to be a challenging NP-complete problem and the discussed results are proven to be helpful in its characterization among various graphs.