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Non-observation of any dark matter signature at various direct detectionexperiments over the last decade keeps indicating that immensely popular WIMPparadigm may not be the actual theory of particle dark matter. Non-thermal darkmatter produced through freeze-in is an attractive proposal, naturallyexplaining null results by virtue of its feeble couplings with the StandardModel (SM) particles. We consider a minimal extension of the SM by two gaugesinglet fields namely, a $\mathbb{Z}_2$-odd fermion $\chi$ and a pseudo scalar$\tilde{\phi}$, where the former has interactions with the SM particles only atdimension five level and beyond. This introduces natural suppression in theinteractions of $\chi$ by a heavy new physics scale $\Lambda$ and forces $\chi$to be a non-thermal dark matter candidate. We have studied production of $\chi$in detail taking into account both ultra-violate (UV), infra-red (IR) as wellas mixed UV-IR freeze-in and found that for $10^{10}{\rm GeV}\leq\Lambda\leq10^{15}{\rm GeV}$, $\chi$ is dominantly produced via UV and mixed UV-IRfreeze-in when reheat temperature $T_{RH}\gtrsim 10^4$ GeV and below which theproduction is dominated by IR and mixed freeze-in. Furthermore, we haveconsidered the cascade annihilation $\chi\bar{\chi} \rightarrow\tilde{\phi}\tilde{\phi}\rightarrow 4\gamma$ to address the longstanding$\sim3.5$ keV X-ray line observed from various galaxies and galaxy clusters. Wehave found that the long-lived intermediate state $\tilde{\phi}$ modifies darkmatter density around the galactic centre to an effective density $\rho_{eff}$which strongly depends on the decay length of $\tilde{\phi}$. Finally, theallowed parameter space in $\Lambda-g$ plane ($g$ is the coupling between$\chi\bar{\chi}$ and $\tilde{\phi}$) is obtained by comparing our result withthe XMM Newton observed X-ray flux from the centre of Milky Way galaxy in$2\sigma$ range.

Fermionic dark matter via UV and IR freeze-in and its possible X-ray signature