I think that the narrative of your post suffers from discontinuity as well as ambiguity. "Overlapping of last working day in previous Company and joining date in current Company" would indicate factually that the date of relief from the previous company and the date of joining in the present Company is one and the same. On the contrary, the actual dates of relief and joining are 01-12-2017 and 26-10-2017 respectively. How is it possible? Last working day in Company X, as per its official relieving letter, is 01-12-2017 would imply that you had been in the service of X up to and inclusive of that date. Your first working day in Company Y being 26-10-2017 would show that you have been in the service of Y from that date. As it is, in essence, it amounts to dual employment which is not practically possible apart from being illegal. Therefore, in reality, there is no overlapping in relieving and joining dates but overlapping of your very employment in both the Companies during the period from 26-10-2017 to 01-12-2017. It leads to the inescapable conclusion that actually you switched jobs unauthorisedly between the two Companies. Perhaps it might be a hasty decision taken by you in the heat of the moment caused by the urgency of Company Y and unwillingness of Company X. Certainly this inexplicable fact would affect your future employment.
16th May 2019 From India, Salem