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Optical follow-up observations of optical afterglows of gamma-ray bursts arecrucial to probe the geometry of outflows, emission mechanisms, energetics, andburst environments. We performed the follow-up observations of GRB 210205A andZTF21aaeyldq (AT2021any) using the 3.6m Devasthal Optical Telescope (DOT)around one day after the burst to deeper limits due to the longitudinaladvantage of the place. This paper presents our analysis of the two objectsusing data from other collaborative facilities, i.e., 2.2m Calar AltoAstronomical Observatory (CAHA) and other archival data. Our analysis suggeststhat GRB 210205A is a potential dark burst once compared with the X-rayafterglow data. Also, comparing results with other known and well-studied darkGRBs samples indicate that the reason for the optical darkness of GRB 210205Acould either be intrinsic faintness or a high redshift event. Based on ouranalysis, we also found that ZTF21aaeyldq is the third known orphan afterglowwith a measured redshift except for ZTF20aajnksq (AT2020blt) and ZTF19abvizsw(AT2019pim). The multiwavelength afterglow modelling of ZTF21aaeyldq using theafterglowpy package demands a forward shock model for an ISM-like ambientmedium with a rather wider jet opening angle. We determine circumburst densityof $n_{0}$ = 0.87 cm$^{-3}$, kinetic energy $E_{k}$ = 3.80 $\times 10^{52}$ ergand the afterglow modelling also indicates that ZTF21aaeyldq is observedon-axis ($\theta_{obs} < \theta_{core}$) and a gamma-ray counterpart was missedby GRBs satellites. Our results emphasize that the 3.6m DOT has a uniquecapability for deep follow-up observations of similar and other new transientsfor deeper observations as a part of time-domain astronomy in the future.

Revealing nature of GRB 210205A, ZTF21aaeyldq (AT2021any), and follow-up observations with the 4K$\times$4K CCD Imager+3.6m DOT