\documentclass{article}

\setcounter{secnumdepth}{4}% Number up to \paragraph

\makeatletter
\renewcommand{\thesubsubsection}{\arabic{subsubsection}}
\renewcommand{\p@subsubsection}{\thesubsection.}
\renewcommand{\theparagraph}{\arabic{paragraph}}
\renewcommand{\p@paragraph}{\thesubsection.\thesubsubsection.}
\renewcommand{\@seccntformat}[1]{%
  \csname the#1\endcsname
  \ifnum\pdfstrcmp{#1}{subsubsection}=0 .\fi% If this is a subsubsection, add a period
  \ifnum\pdfstrcmp{#1}{paragraph}=0 .\fi% If this is a paragraph, add a period
  \quad}
\makeatother

\usepackage[nameinlink]{cleveref}

\crefformat{paragraph}{#2#1#3}

\begin{document}

\tableofcontents

\section{My Section}

\subsection{My subsection}

\subsubsection{My subsubsection}\label{sssec:mysubsubsection}

My section ref is: \Cref{sssec:mysubsubsection}.

\paragraph{My paragraph}\label{par:myparagraph}

My paragraph ref is: \Cref{par:myparagraph}.

\end{document}