  In this paper, we investigate the affine ageing algebra
$\widehat{\mathfrak{age}}(1)$, which is a central extension of the loop algebra
of the 1-spatial ageing algebra $\mathfrak{age}(1)$. Certain Verma-type modules
including Verma modules and imaginary Verma modules of
$\widehat{\mathfrak{age}}(1)$ are studied.Particularly, the simplicity of these
modules are characterized and their irreducible quotient modules are
determined. We also study the restricted modules of
$\widehat{\mathfrak{age}}(1)$ which are also the modules of the affine vertex
algebra arising from the 1-spatial ageing algebra $\mathfrak{age}(1)$. We
present certain constructions of simple restricted
$\widehat{\mathfrak{age}}(1)$-modules and an explicit such example of simple
restricted module via the Whittaker module of $\widehat{\mathfrak{age}}(1)$ is
given.
