  Let $G = (V,E)$ be a connected simple graph of order $p$ and size $q$. A
bijection $f:V(G)\cup E(G)\to \{1,2,\ldots,p+q\}$ is called a local antimagic
total labeling of $G$ if for any two adjacent vertices $u$ and $v$, we have
$w(u)\ne w(v)$, where $w(u) = f(u) + \sum_{e\in E(u)} f(e)$ and $E(u)$ is the
set of incident edge(s) of $u$. The local antimagic total chromatic number,
denoted $\chi_{lat}(G)$, is the minimum number of distinct weights over local
antimagic total labeling of $G$. In this paper, we provide a correct proof and
exact local antimagic total chromatic number of path and spider graphs given in
[Local vertex antimagic total coloring of path graph and amalgamation of path,
{\it CGANT J. Maths Appln.} {\bf 5(1)} 2024, DOI:10.25037/cgantjma.v5i1.109].
Further, we determined the local antimagic total chromatic number of spider
graph with each leg of length at most 2. We also showed the existence of
unicyclic and bicyclic graphs with local antimagic total chromatic number 3.
