In this comprehensive research, the \(^{8}\text {Be}\) , \(^{28}\text {Si}\) , \(^{58}\text {Ni}\) , and \(^{90}\text {Zr}\) accompanied ternary fission of the \(^{244}\text {Fm}\) isotope has been investigated. Calculations were performed considering the equatorial and the collinear geometries. Using the Three-Cluster Model ( \(\text {TCM}\) ) based on the WKB approximation, various quantities including the fission Q-values, driving potentials ( \(\text {V-Q}\) ), penetration probabilities ( \(\text {P}\) ), relative yields, decay constants ( \(\lambda\) ), and fission half-lives were calculated for every fixed fragments with a wide range of fragment combinations which has a positive reaction Q-value. After a systematic analysis, combinations with higher \(\text {Q}\) -values and significant yields were selected for further examination. To provide an in-depth analysis, not only the calculated results for each fixed fragment are tabulated, but also driving potentials, penetration probabilities, and relative yields plotted against the mass number of the fragment ( \(A_{1}\) ). This study highlights the significant role of shell effects, especially for produced fragments with closed-shell neutrons and/or protons magic numbers. Additionally, calculated results underscore the impact of the fragment geometry in the exit channel. The calculated results offer valuable insights for future investigations in nuclear physics, particularly in understanding the nuclear structure and its effect on the complex dynamics of nuclear ternary fission.
