Using Drop 2 or 3 on guitar offers the guitarist a variety of ways to use 4 adjacent strings for the comfortable, if not faster, way to play chords. Yes the chords are inverted. This brings us to chords with more than 4 notes like an A13th. The chord spelled A C# E G B D F#. Based upon other comments lets omit the 11th because of the clash with the 3rd and we still have 6 notes. How do we accomplish the 13th in either a Drop 2 or 3 and in 4 notes?
The main notes needed for a 13th (usually dominant 13th) are root, 3rd, ♭7th and 13th. Root as without it there's no chord name, 3rd defined major /minor, ♭7 gives the tritone definitive to any dominant chord, and 13th - without it, it's not a 13th!
So, 1, 3 ♭7 and 13 (6) are the 4 notes needed to remain. After all, 7+6=13...
The two most common ways to play a 13th chord on the guitar are the ones with the root on the E string and on the A string. E.g., for an A13 you'd get (from low E to high e):
5 X 5 6 7 X (1 7 3 13)
5 X 5 6 7 7 (1 7 3 13 9)
where the second option adds the 9th on the high e-string.
For the root on the A string you'd have
X 12 11 12 12 14 (1 3 7 9 13)
Another slightly less common voicing with root on the E-string is
5 X 5 4 2 2 (1 7 9 3 13)
There are many others if we don't require the voicing to include the root, or to have it as its lowest note, such as
X 10 11 11 10 X (7 3 13 1)
X 10 11 11 12 X (7 3 13 9)
X 4 5 4 7 X (3 7 9 13)
To play extended chords with only four notes, it is typical to leave out the fifth, and some of the middle extensions. So to play a 13th, you'd play the 1 and 3, one of the extensions (preferably the 7), and the 13. For A13, that leaves you with these options:
1 3 7 13 -> A C# G F# 1 3 9 13 -> A C# B F# 1 3 11 13 -> A C# D F#
You mention omitting the 11 because of the clash with the 3, but if you drop the 11, that interval inverts to a less problematic major seventh, and you get:
11 1 3 13 -> D A C# F#
which seems to me to be the easiest drop-2 or drop-3 voicing for this; all other options have a large interval between adjacent strings, or a second between the lowest strings, which isn't ideal either.
You already have some useful information in the other answers, especially @Matt_L who gives specific voicings that work well. I’d like to add a few more points.
Because of the number of strings and the limited way we can anatomically play notes on the fretboard, the guitar doesn’t really use “drop” voicings much. A better term might be “omit” voicings. We have to choose and use only the most useful notes to outline a chord which has already been explained in other answers here. In this case that is R,3,7,13 unless you have a bass player covering the root in which case you have the option to leave it out.
If you want to experiment with creating your own voicings there are a few things to be aware of in order not to have a dissonant sounding chord.
- The 13 should be higher than the 7
- The 9 should be higher than the 3
This will avoid any b9 intervals and also put the fundamental chord tones lower where they generally sound better.
You are correct about the 11 in these chords. The 11 should be omitted from major chords that go to 13. However, sometimes a #11 is added to 13 chords, specially in jazz. It is not uncommon to have 9, #11, 13 in a dominant or major 7th chord. This creates a Lydian sound. It is however very difficult to get them all into a single voicing on the guitar for reasons already covered. One rootless voicing of A13(#11) is X,10,11,8,7,7 (7,3,#11,13,9). It is basically a B triad over the tritone of the A7 chord.