Thank you. but on internet at first sight/first glance both are used. I am giving you a link.If you mean the story initially seemed bogus, then the only version I would use is "at first sight" (without "the").
Thanks for the clarification. I will keep that in mind.Yes, "at first glance" is also used, but in my opinion it doesn't suit this context.
Well, although both "sight" and "glance" have a visual origin, I think we are more likely to extend our use of "at first sight" to contexts where the seeing element is absent (I presume the speaker here did not see "his story", but heard it), whereas we'd keep "at first glance" when there is an actual glance involved.