The literature suggests that there is a strong positive relationship between emotional intelligence and self-efficacy. Emotional intelligence is a predictor of self-efficacy, which itself has a strong relationship with academic achievement. This is to some extent intuitive, as the qualities of emotional awareness and empathy lead to and may explain self-efficacy. In response to your tag of emotional intelligence as a tool for supporting IQ, another question is whether IQ is a good predictor of academic performance. The literature does not support that IQ alone is a strong predictor of academic performance. Perhaps a more relevant question might be to what extent training and intervention on emotional intelligence has on self-efficacy, and whether there is commensurate improvement in academic performance.
You may find interesting some of the research conducted by Dr Hasha Perera, whose profile I have linked below along with a paper titled "The relationship of trait emotional intelligence with academic performance: A meta-analytic review"
https://www.researchgate.net/profile/Harsha_Perera3
https://www.researchgate.net/profile/Harsha_Perera3
http://www.sciencedirect.com/science/article/pii/S1041608013001143
Emotional Intelligence is a trait characteristic to an extent though it could be improved, it has been linked with significant empirical evidence to life and work-place success but not to school success. Self-efficacy on the other hand is a self-perception. Self-efficacy has been linked to school success in several studies(you could check references in one of my articles). I don't think there would be a significant relationship between the two constructs.
https://eduimed.usm.my/EIMJ20201202/EIMJ20201202_03.pdf
Check this out.
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