Is there a 10/100M Ethernet (Fiber/Copper) PHY IP core for Cyclone IV E or Cyclone V

Probably You're missing something. There should be such port. Check the manual.

According to the IP core user guide, the output of the module is 1.25Gbps MDI interface signals,they are: ref_clk, rx_p and tx_p.

Oh You need only 10/100... rx_p/tx_p signals will have negative pair member, when You'll select LVDS or other differential signaling type in pin planner.

Because the IP core interface is 1.25Gbps, I think it can not be supported by Cyclone IV E.

You can't have PHY part in FPGA, which doesn't have transceivers. Basically, even if it has, the PHY part is usually external.

We had a design with Cyclone II, which implements a 10/100M MAC and PHY for fiber port on FPGA without using an external PHY.

I would like to know if there is a commercial / free PHY IP core for Ethernet Fiber/Copper port.

I don't see how the RX PLL for a fibre PHY should be implemented in Cyclone II, perhaps you can tell the name of PHY IP you have used. In any case, there's no Altera (or a competitor's) FPGA that incoprporates the 10/100 MBit ethernet "copper" interface. The only copper interface supported by Altera FPGA on-board hardware so far is a 1000BASE-CX "short haul copper" interface, not compatible with the industry standard 1000BASE-T twisted pair interfaces.

Sorry, I do not understand your answer.