A Diophantine problem with a prime and three squares of primes

We prove that if ${\lambda }_1$, ${\lambda }_2$, ${\lambda }_3$ and ${\lambda }_4$ are non-zero real numbers, not all of the same sign, ${\lambda }_1\mathrm{/}{\lambda }_2$ is irrational, and $\varpi$ is any real number then, for any $\text{eps}>0$ the inequality $ \bigl|\lambda_1 p_1 + \lambda_2 p_2^2 + \lambda_3 p_3^2 + \lambda_4 p_4^2 + \varpi \bigr| \le \bigl(\max_j p_j \bigr)^{-1 / 18 + \eps} $ has infinitely many solution in prime variables $p_1$, …, $p_4$