As per NFPA - 101, 7.1.5 "Means of egress shall be designed and maintained to provide headroom in accordance with other sections of this code, and such headroom shall be not less than 7 ft 6 in. (2285 mm). Projections from the ceiling shall provide headroom of not less than 6 ft 8 in. (2030 mm), with a tolerance of −3∕4 in. (−19 mm)…", Headroom for staircase is shall not be less than 1980 mm. or 2030 mm.
What would be the minimum height, to be considered in egress path for ordinary hazard !