The phrase "by or at the side of" represents a proximity or adjacency to something or someone. There are many synonyms for this phrase that can be used interchangeably, depending on the situation. Some examples include "beside," "adjacent to," "alongside," "proximate to," "near," "close to," "flanking," and "next to." These synonyms can be used in a variety of contexts, from describing the location of physical objects to referring to the presence of someone nearby. Whatever synonym you choose, its purpose is to enhance the clarity and specificity of your writing by providing a more precise way to convey information about the location or situation.