The central ambition based on this article inhabit to nominate the conception based on a neutron \({S}_{\beta }^{F}\) -conn spc in NTS. Moreover, some properties of the neutron \({S}_{\beta }^{F}\) -conn spc have been proposed with suitable illustrations. The theorems like “If a NTS \( \left( {X_{\mathcal{N}eut} ,\tau } \right) \) is neutron \({S}_{\beta }^{F}\) -conn spc between the NSs \(A\) together with \(B\) , then it is neutro conn spc between \(A\) together with \(B\) ”. Further the inverse of the above theorem is not accurate in general are proved with suitable illustration. Moreover, many essential theorems based on the neutron \({S}_{\beta }^{F}\) -conn spc have been proved. In addition, various relevant theorems based on the operators like neutron \({S}_{\beta }^{F}\) -closure have been demonstrated. Further, a new concept based on a neutron \({S}_{\beta }^{F}\) -FCS in a NTS have been proposed and studied with proper illustration. Moreover, using the theory of neutron \({S}_{\beta }^{F}\) -CS a new concept based on a neutron \({S}_{\beta }^{F}\) -FSCS is introduced and studied with proper illustration. Further the theorems connecting neutron \({S}_{\beta }^{F}\) -FCS and neutro \({S}_{\beta }^{F}\) -FSCS have been proved and illustrated. In addition, a relationship between a neutron \({S}_{\beta }^{F}\) -conn spc, neutron \({S}_{\beta }^{F}\) -FCS and neutron \({S}_{\beta }^{F}\) -FSCS have been studied with proper illustration as shown below in Fig. 1. Several theorems based on the above concepts have been justified.