Quasi-syllogism is a categorical syllogism where one of the premises is singular, and thus not a categorical statement.
For example:
All men are mortal Socrates is a man Socrates is mortal
In the above argument, while premise 1 is a categorical, premise 2 is a singular statement referring to one individual. While this is a valid logical form, it is not strictly a categorical syllogism.
Of course, it has been suggested that you can translate any singular statement into a categorical.
For example:
Socrates is a man All members of a class of which the only member is Socrates are men
The above two premises may be considered identical, but the first is a singular and the second is a categorical.
See also Transitivity of hyponymy Type of syllogism (disjunctive, hypothetical, legal, poly-, prosleptic, quasi-, statistical)
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