H^{s-1}$, $s_{c} \leq s <1$) and in dimension $3$ has been recently studied in [@triroyradnlkg] for radial data. More precisely it was proved that the asymptotic behaviour is linear for $3<p<5$ and for radial data in $H^{s} \times H^{s-1}$, $ s_{p} < s < 1$ with

$$\begin{array}{l}
s_{p} := \left\{
\begin{array}{l}
1- \frac{(5-p)(p-3)}{2(p-1)(p-2)}, \, 4 \geq  p > 3 \\
1- \frac{(5-p)^{2}}{2(p-1)(6-p)}, \, 5 > p \geq 4
\end{array}
\right. \end{array}$$

In this paper we are interested in proving scattering results for general data below the energy norm and in dimension $3$. The main result of this paper is the following one

Let $3<p<5$. Let $(u_{0},u_{1}) \in H^{s} \times H^{s-1}$ and $A \geq 0$ such that

$$\begin{array}{ll}
\|( u_{0},u_{1}) \|_{H^{s} \times H^{s-1}} & \leq A
\end{array}
\label{Eqn:BoundA}$$

Then there exists $\tilde{s}:=\tilde{s}(A,p) < 1$ such that the solution of the $p$-defocusing Klein-Gordon equation on $\mathbb{R}^{3}$ with data $(u_{0},u_{1})$ exists for all time $T$ in $ H^{s} \times H^{s-1} $, $ 1> s > \tilde{s}$. Moreover it scatters as $T$ goes to infinity, i.e there exists $\left( u_{+,0}, u_{+,1} \right) \in H^{s} \times H^{s-1}$ such that

$$\begin{array}{ll}
\lim \limits_{T \rightarrow \infty} \| \left( u(T) , \partial_{t} u(T) \right) - K(T) (u_{+,0}, u_{-,0} 