This often happens. A defender sees the final contract, thinks they are on opening lead and plays a card, but partner is actually on lead.
It helps to make the opening lead face down, partner will stop you from facing the card and it can be withdrawn (but call the Director).
If the wrong defender makes a faced opening lead then Declarer has FIVE options :
A. Accept the incorrect lead and play on. Dummy goes down as normal, but the next card is played from Declarer's hand.
B. Accept the incorrect lead and have partner become Declarer. Your hand goes down as dummy and plays next.
Otherwise, we don't accept the lead and the lead reverts to the correct defender.
And now we deal with the incorrect lead as a major penalty card :
C. Demand the lead of the suit of the penalty card. The penalty card can be picked up and restored to the hand, and doesn't have to be played to this trick.
D. Forbid the lead of the suit of the penalty card. The penalty card can be picked up and restored to the hand. This prohibition may continue for as long as the non-offending defender remains on lead.
E. Allow any suit to be led. The illegal faced card remains a major penalty card, has to be played at the first legal opportunity, and lead restrictions can still be applied later.
Law 54 - Faced Opening Lead out of Turn
Law 50D - Disposition of a Major Penalty Card
NZ Bridge flowchart for all Leads out of Turn
NZ Bridge flowchart for all Penalty Cards
Example
North bids 1NT, South 3NT. West leads the 4 of hearts face up. East is meant to be on opening lead.
North has FIVE options. They can accept the lead and just play on, South goes down as dummy, North plays next (A). They can accept the lead and put North down as dummy, South becomes Declarer and plays next from North (B).
Or they can not accept the lead and the 4 of hearts becomes a major penalty card. Now North can demand a heart lead, and the 4 gets picked up (C); forbid a heart lead and the 4 gets picked up (and continue to forbid a heart if East remains on lead) (D); or allow East to make any lead and the 4 of hearts remains face up on the table (E).
Further thoughts
Defenders are allowed to ask "Is it my lead ?"
Defenders are not actually allowed to say "It's your lead partner."
Declarer/Dummy should refrain from telling a defender it is their lead. If Declarer does incorrectly tell a defender that it is their lead, and they lead face up, it can be withdrawn (Law 47E).
Always make your opening lead face DOWN, and wait for your partner to say "Thanks". This gives partner a chance to say "No, it's my lead". It also gives partner a chance to ask questions about the auction - they can't ask questions when you are about to lead, obviously, giving you hints.
Declarer doesn't have to warn you that your face-down card is from the wrong hand.
The Director should always be called if the face-down card is wrong. The defenders may have some nefarious system. Even without an illegal agreement, the quick play of an opening lead looks like a singleton, or maybe top of a sequence, and the information is unauthorised.
Partner of Declarer cannot offer any advice about the options.
If Dummy starts spreading their cards face up, this becomes the option that Declarer must choose. The Director should still be called as this could be an unethical action by dummy.
If Declarer starts spreading their cards face up, this has become their choice, they become dummy.
If Declarer chooses to demand a lead of the penalty card, and the defender doesn't have a card of that suit (the Director will check), they can lead any card (Law 59). The penalty card is picked up.
If the exposed card is picked up, knowledge of that card is "unauthorised" to the partner. They cannot take advantage from knowing their partner has that exposed card. The Director can even adjust the score if they do take advantage.
Declarer cannot demand another suit be led. They can only demand or forbid the suit of the exposed card.
Advice - which option should you take ?
What is the faced opening lead ? Is it a strong card from top of a sequence, or maybe a singleton ? Is it a suit they bid, or a suit their partner bid ? Why did they lead so hastily ?
Do you like the lead ? If you don't mind the lead, and maybe another suit is more dangerous, then accept the lead. If partner has shown a stopper in the suit, you probably prefer this suit to be lead. And now you have the choice of being declarer or dummy. Do you want your hand exposed to the defenders, or partners ? If you have hidden strengths then it may be best to stay as declarer. If partner has opened 1NT or 2NT then you probably want their hand hidden as declarer. If partner has the stronger hand, let them be Declarer.
You may like the suit lead, but from the other side of the table, which you can demand. Maybe you have Kx or AQ in that suit which guarantees a trick on the lead (remembering that the offending lead card doesn't have to be played).
If you don't like the suit, then it's probably best to not accept the lead, and forbid the suit. Remembering also that you can continue this prohibition if the opening leader wins the first trick.
If the faced lead is a significant card, e.g. the ace of trumps, you might take the option to not accept the lead, and then allow the other defender to lead any suit, retaining the ace as a major penalty card. Now it has to be played at the first legal opportunity, which you can use to your advantage. If it is a non-trump ace you might be able to force it to be discarded ! Or similarly in a no-trump contract, you win the lead and run your long suit, and the penalty card has to be discarded.
If it's a small card, you could leave it on the table and then take a finesse against the other defender, knowing the small card will have to be played as the last card to the trick.