\theta_{23} = \frac{\pi}{4}$ and different values of $\theta_{12}$ depending upon the particular realisation of this symmetry [@Xing:2015fdg], has already been ruled out by recent neutrino experiments. Among such realisations, the tri-bimaximal (TBM) mixing [@Harrison:2002kp; @Xing:2002sw; @Harrison:2002et; @Harrison:2003aw; @Harrison:2004he] which predicts $\theta_{12}=35.3^o$ has been the most popular one. This mixing, which was consistent with neutrino data before the discovery of non-zero $\theta_{13}$ can be realised naturally within several flavour symmetric models based on non-Abelian discrete groups [@Ishimori:2010au; @Grimus:2011fk; @King:2013eh; @Altarelli:2010gt]. Among such flavour symmetric models, the discrete group $A_4$, group of even permutations of four objects, can reproduce the TBM mixing in the most economical way [@Ma:2001dn; @Babu:2002dz; @Hirsch:2003dr; @Ma:2004zv; @Ma:2004zd; @Chen:2005jm; @Ma:2005sha; @Zee:2005ut; @Ma:2005mw; @Ma:2005qf; @Altarelli:2005yx]. However, in order to be consistent with the present neutrino data, such TBM or $\mu-\tau$ symmetric scenarios have to be corrected to generate non-zero value of $\theta_{13}$. There have been several attempts in that direction, some of which can be found in [@Kang:2005bg; @Shimizu:2011xg; @King:2011zj; @Antusch:2011ic; @King:2011ab; @Gupta:2011ct; @Ge:2011qn; @Ge:2010js; @Ge:2011ih; @Liao:2012xm; @Xing:2010pn; @Adhikary:2006wi; @Ma:2011yi; @Altarelli:2012bn; @Karmakar:2014dva; @Chen:2012st; @Borah:2013jia; @Borah:2013lva; @Borah:2014fga; @Borah:2014bda; @Kalita:2014mga; @Mukherjee:2017pzq; @Borah:2017qdu] and references therein.

Apart from non-zero neutrino mass and large leptonic mixing, another observed phenomena that has propelled serious 