Correlation and correlation coefficients are the most utilized statistical tools and measures in the field of engineering, intelligence sciences, data analysis, decision making, biological sciences, etc: In the present communication, we have proposed two new measures of correlation coefficients and measures of weighted correlation coefficients of two T-spherical fuzzy sets based on the newly defined information energy measure under the perception of the four parameters of impreciseness - degree of membership, indeterminacy (neutral), non-membership and the refusal. Further, by implementing the principle of maximum correlation coefficient over the proposed correlation coefficients, the methodologies for solving the problems of pattern recognition and medical diagnosis have been provided with the help of an example for each. A comparative analysis in contrast with the existing methodologies has been presented with comparative remarks and additional advantages.