  We study chiral algebras in the $\bar{Q}$-cohomology of two dimensional SYK
models with extended supersymmetry. In a special limit discovered in
arXiv:1805.09325, we are able to construct explicitly a "vertical"
single-particle higher-spin algebra that is bilinear in the fundamental fields.
This algebra can be regarded as the counterpart, when going away from
criticality, of the infrared emergent higher-spin symmetry of the
$\mathcal{N}=(0,2)$ SYK model. Moreover, a second "horizontal" single-particle
higher-spin algebra appears in this limit. Together with the vertical algebra
they generate a stringy algebra with a "higher spin square" structure that is
believed to appear in the tensionless limit of string theory. On the other
hand, we do not find single-particle higher-spin algebra away from the special
limit, which is consistent with the result in arXiv:1805.09325. Our analysis is
carried out for each individual realization of the random couplings and for
finite $N$ (and $M$), which in particular indicates that the conclusion in
arXiv:1805.09325 is robust to $1/N$ corrections.
