  In this paper we constructs a new nontrivial family in the stable homotopy
groups of spheres $\pi_{p^nq+2pq+q-3}S$ which is of order $p$ and is
represented by $k_0h_{n} \in Ext_A^{3,p^nq+2pq+q}(\mathbb{Z}_p,\mathbb{Z}_p)$
in the Adams spectral sequence, where $p\geq 5$ is an odd prime, $n\geq 3$ and
$q=2(p-1)$. In the course of the proof, a new family of homotopy elements in
$\pi_{\ast}V(1)$ which is represented by
$\beta_{\ast}{i^{\prime}}_{\ast}i_{\ast}({h}_n)\in
Ext_A^{2,p^nq+(p+1)q+1}(H^{\ast}V(1),\mathbb{Z}_p)$ in the Adams sequence is
detected.
