Are there any legitimate 5e spells/items/mechanics that reproduce the effect of the Psychic Paper from Doctor Who?
A 6th-level Illusion Wizard with Illusory Script, Detect Thoughts, and Forgery Kit proficiency
Illusion Wizards get access to the following feature at 6th level:
Malleable Illusions. Starting at 6th level, when you cast an illusion spell that has a duration of 1 minute or longer, you can use your action to change the nature of that illusion (using the spell's normal parameters for the illusion), provided that you can see the illusion.
Combined with Illusory Script, this feature can be used to, as just a single action (and without any spell components that would make that action conspicuous), change the text on a Illusory-Script-ed piece of paper they can see.
So, as this Wizard, you can:
- Cast Illusory Script on a piece of paper. It doesn't matter what the original script says - designate no other creatures who can see the true script, so that all other creatures (without truesight) will see the illusory script. This is your "psychic paper".
- Cast Detect Thoughts out of sight of the gatekeeper/whoever you're trying to fool.
- Walk up to them demanding entrance. Use Detect Thoughts to guide your claims about who you are.
- When they ask for proof of your authority, get out your "psychic paper", unfolding it facing you. Use their surface thoughts about what they would expect to see on a document which actually proved your claims to guide your Malleable-Illusion changes to what the script says.
- Show your "psychic paper" to the gatekeeper. It says whatever they expected it would if it were legitimate.
The Forgery Kit proficiency is just bonus - as a DM I would rule this trick more likely to work if the wizard was also a skilled forger, as the result of their on-the-fly illusion change could then be even more authentic. Illusory script states the writing is "in your own hand" - so if the gatekeeper was expecting a specific hand he would recognise, being able to forge that (for a forger, "in your own hand" can become "in any hand you can forge with your own hand") might be a necessity rather than just a bonus.
Blank Paper and suggestion
Ultimately, the Doctor is simply convincing someone that the paper says something that makes sense to the viewer.
This can be done with the spell suggestion:
You suggest a course of activity (limited to a sentence or two) and magically influence a creature you can see within range that can hear and understand you. Creatures that can't be charmed are immune to this effect. The suggestion must be worded in such a manner as to make the course of action sound reasonable. Asking the creature to stab itself, throw itself onto a spear, immolate itself, or do some other obviously harmful act ends the spell.
Is this a Course of Action?
The potential problem here is in how to interpret "course of action". Usually that implies that the suggestion is making the target "do" something. Whether or not "You read this paper to show that I'm [X]" is considered a 'course of activity' will be up to a DM to determine, but I'm having a hard time coming up with a good reason why it wouldn't work.
Is the Course of Action Reasonable?
These aren't the droids This is the paper that you're looking for
Suggestion still has the requirement that the course of action is reasonable. That's always the tricky part with this spell and can very much depend on DM decision.
But, one way that seems passable (to me as a DM), would be to suggest:
The paper you see provides credentials that will allow me past. You see this and allow me past.
At this point, you've made the potentially reasonable suggestion that they see exactly what they expect to see from someone they'd allow past. And then would do so because their narrative of why they'd allow you to pass has been met.
Basically, it's reasonable that they'd have visitors they allow past. They know who those visitors are. You are planting the suggestion that you are one of those visitors.
Difference from Psychic Paper
The big difference here is that you do need to 'prompt' the target as to how to read the paper. I think it still works from a Doctor Who lore perspective for suggestion to cover this, but it is a little bit clunkier.