  In the present paper we prove that every sufficiently large odd integer $N$
can be represented in the form \begin{equation*} N=p_1+p_2+p_3\,,
\end{equation*} where $p_1,p_2,p_3$ are primes, such that $p_1=x^2 + y^2 +1$,
$p_2=[n^c]$.
