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The authors investigated four different fin geometries to select the best fin geometry in their previous work. They found out that the Nusselt number of the shell side is 80.79% higher for the stepped fin geometry compared to the simple annular fin at best. In this study, for the first time the heat transfer in a shell and helically coiled finned tube heat exchanger with stepped annular fins is investigated. The coiled tube and the stepped ring fins that are welded to the outside surface of the tube are all made of copper. After examining network independence, 27 cases were designed using Response Surface Methodology (RSM). Correlations have been proposed to predict Nuc$N{u}_c$ and Nush$N{u}_{sh}$ by considering all geometric and operating parameters. These correlations have very high accuracy and can be used in a specific range of parameters. The effect of each of the parameters on Nuc$N{u}_c$ and Nush$N{u}_{sh}$ are also specified. Re${\mathop{\rm Re}\nolimits} $ and Pr$\Pr $ are the parameters that have the most impact on the Nusselt number on the same side, but at the same time have almost no effect on the Nusselt number on the other side. Rec${{\mathop{\rm Re}\nolimits} }_c$ and Resh${{\mathop{\rm Re}\nolimits} }_{sh}$ have the highest participation rate in determining Nuc$N{u}_c$ and Nush$N{u}_{sh}$ with 82.62% and 71.13%, respectively. The results are presented based on dimensionless parameters. The optimization process is performed for each of the responses, and the values ​​of the corresponding parameters are also shown. Nush$N{u}_{sh}$, which is the most critical response in this study, has improved 19.59% in the optimized case, even compared to the best of the 27 cases studied. To have the best overall heat performance of the heat exchanger, the optimization process has been performed.