Prepositions are words which show the relationship between a noun or a pronoun object and some other words (predicates) in the sentence.
ASL doesn't use these prepositions such as "on", "in", "under", etc. as much as English does. Prepositions are expressed richly in various ways in sign language using classifiers, locatives, agreement verbs, spatial referencing, and more.
Prepositions in ASL may be occasionally used in some contexts but not in most cases. Many prepositions are embedded in verb phrases (predicates) in ASL, often using classifiers, locatives, and such.
Locatives in sign language are used to describe a spatial relationship between two or more objects and/or persons. They indicate where the objects or persons are or how they are located in relation to other objects and/or persons. Locatives are equivalent to prepositions in English, such as: in, outside, on, next to, at, from, behind, above, under, etc.
Prepositions are expressed in sign language using locative classifiers. Classifier is a pronoun-like linguistic symbol that represents a class or group of referents. In ASL, a noun should be signed first before using its classifier to refer to it until a subject or noun is changed.
The signer uses a classifier and movement for the ASL word leak. This classifer (handshape) refers to some kind of liquid and the location of the hand indicates where the leak occurs. [L] The signer signs leaking from the cup. She also uses the classifier for the "cup" with the other hand. [M] She signs bleeding or leaking from the nose. [R] You can guess -- leaking or bleeding from the ear. The signer would first sign a noun, such as "blood", "tea", or another kind of liquids before she proceeds to using classifiers for these nouns.
The signer begins with the ASL word table [left image] and then assigns it a pronominal classifier (palm faced down) for the table (in the same way that you speak "Ms. Jane Doe is..." and then "she... she..." through the sentences). This classifier can be used to refer to a table, desk surface, etc. She has now established a spatial location for the table.
The signer then utters the ASL word cat (the noun) and immediately assigns it the pronominal classifier [below]. Notice that the signer still holds the pronominal classifier and the location for the table.
The bent 2-handshape, that is the classifier, represents the sitting cat. The locatives show that the cat is sitting below or under the table.
Or, "... sitting on the table".
Or, "... lying down on the table". The signer has changed the palm orientation of the classifier.
Below shows an example of using a pathline of locative classifier. Index finger is the common handshape for a pathline in a verb predicate.
Gloss: ball thrown cl-pathline[medium]
The CL-pathline can be used for the movement or trace of a bird flying across the sky, a horse running around the track, etc.
Below is a few examples of using prepositions, such as: in, outside, on, next to, at, from, behind, above, under, etc.
It means through (the) city. For example, one is driving through a/the city. Though, the word order in ASL in this video above is as follows: city through. The reversed order through city can also work, depending on a sentence (how spatial relation is used with other ASL words).
This can be interpreted in different ways in ASL as all over (the) city or throughout (the) city.