I was is this something that is common in minting process or an error i have blended two photos together to explain what i have noticed.
Is that a T in the 0 of 60 if not what is that and when you put the liberty stamp from the same penny over top of it it matches perfectly even the other letters of the word correspond with other marks on the coin
The word LIBERTY is much bigger in size than what you are superimposing over the date. You make no sense. You are seeing something that is not there.
http://www.error-ref.com/the-mysterious-1960-small-date-lincoln-cent/ There are hundreds of similar but different examples of what i am explaining but this is impossible
You may be looking for something too hard. Don't use a microscope. Just an eye loupe with a slight magnification is sufficient. Not including the small date over large date, the other 3 non Philly small date 1960 cents (1960 large date, 1960-D large date, 1960-D small date) are all worth 1 cent.
If, by imposing the "Liberty" over the date, we are supposed to see it in the other photos you've provided, without the overlay, then I'd have to say, as has been stated earlier, that it's a case of numismatic pareidolia; There is nothing close to LIBERTY over the date, in your other photos. If we're missing something, then please post what the error is on the coin, and what we should be able to see without the overlay you did.
I cannot think of any way this can happen during the minting process. Can't be an overstrike with that alignment, nor could it be an overstruck on an off center cent (rim would be damaged and it probably wouldn't fit in the collar, anyway). All errors and varieties can be explained from the minting process. Yours can't. Remember, the minting process is well understood and documented. Some of the responses you received are from people with a great deal of knowledge of that process. Trust them. If you don't, then provide a plausible explanation on how this could occur at the mint.