It depends what you call color photography. Color photography was first attempted beginning in the 1840s.
However, the three-color method, which is the foundation of virtually all practical color processes whether chemical or electronic, was first suggested in an 1855 paper on color vision by Scottish physicist James Clerk Maxwell. The first color photograph made according to Maxwell's prescription, a set of three monochrome "color separations", was taken by Thomas Sutton in 1861 for use in illustrating a lecture on color by Maxwell, where it was shown in color by the triple projection method.
Color photography began in the nineteenth century Although color photography for the amateur photographer became popular only in the 1930s, its history dates to the very first years of photography. The two French experimenters Niepce and Daguerre, who, with the English Fox Talbot, pioneered black and white photography, tried to reproduce colors in the 1820s. They only managed to produce color photographs by hand-tinting their photographs, called Daguerreotypes and Calotypes. It was the discoveries of the Scots physicist Sir James Clerk Maxwell in 1861 that really enabled color photography to progress.