was the first one replaced?
The Flying Eagle was replaced with the Indian head design.
Indian Head cent
In 1858 the Flying Eagle was replaced with the Indian head design. 
who designed the three-cent silver? James B. Longacre. did they came out in different types? Yes, three types. who struck the cent? The Mint of the United States. where was the engraver of this cent born? Delaware County, Pennsylvania. has he designed any other coins? Indian Head cent, Shield nickel and the Flying Eagle cent.
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Indian Head cent [SEP] Introduction
In 1857 the Mint reduced the size of the cent and changed the composition to 12% nickel and 88% copper (copper-nickel), issuing a new design, the Flying Eagle cent. The new pieces were identical in diameter to modern cents, though thicker. This was the first use of copper-nickel by the United States. The copper-nickel made them look brighter and they began to be called "White cent" or "Nicks". In 1858 the Flying Eagle was replaced with the Indian head design. The Flying Eagle design caused production difficulties and the Mint soon looked to replace it. Mint Director James Ross Snowden selected the Indian Head design and chose a laurel wreath for the reverse that was replaced in 1860 by an oak wreath with a shield.