  In this work we study 35 stellar clusters in the Small Magellanic Cloud (SMC)
in order to provide their mean metallicities and ages. We also provide mean
metallicities of the fields surrounding the clusters. We used Str\"omgren
photometry obtained with the 4.1 m SOAR telescope and take advantage of $(b -
y)$ and $m1$ colors for which there is a metallicity calibration presented in
the literature. The spatial metallicity and age distributions of clusters
across the SMC are investigated using the results obtained by Str\"omgren
photometry. We confirm earlier observations that younger, more metal-rich star
clusters are concentrated in the central regions of the galaxy, while older,
more metal-poor clusters are located farther from the SMC center. We construct
the age-metallicity relation for the studied clusters and find good agreement
with theoretical models of chemical enrichment, and with other literature age
and metallicity values for those clusters. We also provide the mean
metallicities for old and young populations of the field stars surrounding the
clusters, and find the latter to be in good agreement with recent studies of
the SMC Cepheid population. Finally, the Str\"omgren photometry obtained for
this study is made publicly available.
