\lesscong extending amssymb

Here is a generic command for defining such symbols. The internal macro \gl@over takes an optional argument (for a bit of vertical spacing, default 1pt), the < or > symbol and the symbol to go below.

\documentclass{article}
\usepackage{amsmath,amssymb}

\makeatletter
\newcommand{\lesscong}{\mathrel{\gl@over{<}{\cong}}}
\newcommand{\lesssimeq}{\mathrel{\gl@over{<}{\simeq}}}
\newcommand{\gtrcong}{\mathrel{\gl@over{>}{\cong}}}
\newcommand{\gtrsimeq}{\mathrel{\gl@over{>}{\simeq}}}
\newcommand{\gl@over}[3][1pt]{%
  \vcenter{\m@th\offinterlineskip\ialign{%
    \hfil$##$\hfil\cr #2\cr \noalign{\vskip#1} #3\cr
  }}%
}
\makeatother

\begin{document}

\begin{tabular}{ll}
\verb|\lesssim|    & \( A \lesssim B \) \\
\verb|\lessapprox| & \( A \lessapprox B \) \\
\verb|\leqq|       & \( A \leqq B \) \\
\verb|\lesscong|   & \( A \lesscong B \) \\
\verb|\lesssimeq|  & \( A \lesssimeq B \) \\
\verb|\gtrsim|    & \( A \gtrsim B \) \\
\verb|\gtrapprox| & \( A \gtrapprox B \) \\
\verb|\geqq|       & \( A \geqq B \) \\
\verb|\gtrcong|   & \( A \gtrcong B \) \\
\verb|\gtrsimeq|  & \( A \gtrsimeq B \) \\
\end{tabular}

\end{document}

The calculations are left to TeX.

It can be done with some \raiseboxes. The resulting symbol fits well with \lesssim, \lessapprox and \leqq, but it is a bit tall.

What do you think?

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\newlength{\congwidth}
\newlength{\congheight}
\settowidth{\congwidth}{$\cong$}
\settoheight{\congheight}{$\cong$}
\newcommand{\lesscong}{%
    \mathrel{\smash{%
        \raisebox{-.5\congheight}{$\cong$}%
        \hspace*{-\congwidth}%
        \raisebox{.6\congheight}{$<$}%
    }}%
}
\begin{document}
\begin{tabular}{ll}
    \verb|\lesssim|     & \( A \lesssim B \) \\
    \verb|\lessapprox|  & \( A \lessapprox B \) \\
    \verb|\leqq|        & \( A \leqq B \) \\
    \verb|\lesscong|    & \( A \lesscong B \) \\
\end{tabular}
\end{document}