Copy the definition of \paragraph from your class (here I used article) and modify it by just adding \maybe@addperiod as shown: it should be the last token in the last argument.
\documentclass{article}
\usepackage{amsthm} % for \@addpunct
\makeatletter
\renewcommand\paragraph{%
@startsection{paragraph}
{4}
{\z@}
{3.25ex @plus1ex @minus.2ex}
{-1em}
{\normalfont\normalsize\bfseries\maybe@addperiod}%
}
\newcommand{\maybe@addperiod}[1]{%
#1@addpunct{.}%
}
\makeatother
\begin{document}
\paragraph{This is the title} And some text follows.
\paragraph{This is the title.} And some text follows.
\paragraph{Is this is a title?} And some text follows.
\end{document}
As you can see, the period is printed only if punctuation doesn't end the argument to \paragraph.
If you want a version that doesn't need looking for the definition:
\documentclass{article}
\usepackage{amsthm} % for \@addpunct
\makeatletter
\NewCommandCopy\latexparagraph\paragraph
\RenewDocumentCommand{\paragraph}{sO{#3}m}{%
\IfBooleanTF{#1}
{\latexparagraph*{\maybe@addperiod{#3}}}
{\latexparagraph[#2]{\maybe@addperiod{#3}}}%
}
\newcommand{\maybe@addperiod}[1]{%
#1@addpunct{.}%
}
\makeatother
\begin{document}
\paragraph{This is the title} And some text follows.
\paragraph{This is the title.} And some text follows.
\paragraph{Is this is a title?} And some text follows.
\end{document}

\paragraphis a fourth level section heading following section,subsection,subsubsection. Despite its name it doesn't have much to do with paragraphs of text. You could modify the definition copied from article class (which is only a line) or use any package that helps set up section formatting. – David Carlisle Sep 07 '16 at 09:44titlesec, then you can do\titleformat{\paragraph}[runin]{\normalfont\normalsize\bfseries}{\theparagraph}{1em}{}[.]. So if you write\paragraph{A title}, this will yieldA title.in the resulting PDF. – Alenanno Sep 07 '16 at 09:49