The blaze broke out around 1:25 a.m. and was brought under control about an hour later.
Permits for the 100,000-square-foot building were filed this week.
The Eastern Parkway and Franklin Avenue building will have a roofdeck and fitness center.
Myls Dobson, 4, was staying in The Ritz Plaza residences after his father went to jail, relatives said.
The blaze started about 12:45 p.m., FDNY said.
Firefighters worked for about an hour Sunday to extinguish the fire.
Five apartments were badly scorched and many more damaged in the fire on W. 109th St., FDNY said.
The fire at 427 E. 80th Street spread from the basement all the way to the roof, the FDNY said.
The victim was attacked inside 41-01 Vernon Blvd., police said.
The family of four includes 2-month-old Corey, who blacked out during the blaze but has recovered.
There were three firefighters among the injured in the blaze at 2727 University Avenue Wednesday night.
A fire tore through an Inwood apartment building Saturday night, injuring four, officials said.
The View, which has sat empty since the recession, will open for rentals this month.
A man died in a fire at 343 Jefferson Ave. in Brooklyn late Sunday, authorities said.
A fire broke out early Saturday morning in a three-story apartment building in SoHo.
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