The problem with marking cards is that the game will favor players with good memories who don't need to mark the cards or whatever they use at all and therefore don't reveal any information to their opponent. A very advanced player could memorize all the possible marking methods.
You might make something work where each player starts by taking a turn, marking their cards or simply memorizing their layout, then blanking the screen before passing to the next player. Once all players have seen the board, you can put it between all the players and let it go. If the marks are subtle enough and the background complicated enough that an observer won't know (for example, a snowflake background where the player knows one very particular snowflake is theirs, or just a sequence of letters where the player knows one combination represents their mark) you might make it so that even an advanced player can't know which one is the opponent until it's too late and the match is over.
I think you might be thinking of a different kind of card game than I was. (Of course, if you know your own cards and their positions, you can still know your own cards when they're flipped over face-down.)
I was thinking of something more like the following game. Each player would have their own deck (say the numbers 1 to 21 plus four specials), and before play begins each gets two or three minutes alone to scrawl something on the back of their cards (dots, lines, shapes, dongs, whatever). After play begins, however, the cards are dealt at random, face down. Until you actually choose a card to play it, the only information you have about your own cards comes from the marking strategy you invented privately before the game started.
In other words, your pre-game task is to make a "language" describing each card that's easy enough for you to remember under pressure, but hard for an opponent to work out the system.
(Granted, if I have neuro-atypical memory powers and can memorize how 25 completely arbitrary dong drawings map to 25 card possibilities, then I would make a strong opponent. But not necessarily the best opponent, since there are two other parts of the strategy beyond minimizing the obviousness of your own system: figuring out other players' patterns, and setting up apparent (but false) patterns as part of a misdirection strategy.)