4x4 Switch Matrix Problem Please Help
We read in your question that your keypad has different matrix connection order than some other one that you see in a schematic. But it is completely unclear why this is of concern. Here are various situations and how you may work around the issue.


If you are making a product from scratch, including your own circuit boards, microcontroller and firmware then you can program your keypad to operate as you wish. If some type of positional translation of key positions to actual code represented is required then just do it in your firmware.
If you are copying someones design using their circuit board and microcontroller firmware then just wire in the keypad's 8 connections as is. The only thing that changes is the physical position of each one of the buttons. If there is any specific button that needs to be decoded a certain way (i.e. such as when you press the 1  that a '1' shows up on a display) then simply adjust the reference firmware to translate the keypad codes from the keypad scanning module. If you so not have the source code for the reference firmware then quite possibly you may be doing something illegal and should revert to #1 above.
If you are trying to repair an existing unit because the keypad on the device is damaged or missing then you have limited choices. One is to just let the keys of the replacement keypad work as they will map (although if there is a display the key press may not match the display). Another choice is to set aside your keypad and source in another one that has the same mapping as the original. And finally you could use a label printer to print out new button legend stickers which you place on each button of the replacement keypad.