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\documentclass[a4paper, 12pt]{report}
\usepackage{anyfontsize, times, siunitx, ragged2e, setspace, titlesec}
\usepackage{enumitem}
\usepackage{lscape, tabularx, booktabs}
\usepackage{rotating}
\setlength{\parindent } { 10ex }
\doublespacing
%\titleformat{command}[shape]{format}{label}{sep}{before-code}[after-code]
\titleformat{\chapter}[display]{\normalfont\bfseries}{\huge Chapter \thechapter}{2pt}{\Large\bfseries}
\titlespacing{\chapter}{ 0cm }{-3cm }{0.5cm}


\begin{document}
    \chapter{Summary}
Buffaloes contribute significantly to dairy economy by being the major milk producers in Indian subcontinent. Genetic progress in buffalo has been slow as compared to cattle due to low adoption of AI. \section{AI} Poor post thaw semen quality has contributed to poor AI conception rates in buffalo. Buffalo spermatozoa are more sensitive to freezing  as compared to cattle spermatozoa due to a different sperm lipids ratio. 
\subsection{Normality }Application of sub optimum semen freezing protocols standardized in cattle are being used for buffalo cryopreservation . Evaluation of freezing rates for buffalo spermatozoa, reveal finer controls on damage through manipulation of cooling rates at critical temperature zones of freezing
\paragraph{Cost}
Cryopreservation results in temporary, as well, as permanent loss of vitality and viability in more than 50 percent of total sperm, leading to loss of resources. Increasing cost of production and semen sexing has resulted in decrease in number of spermatozoa per insemination dose and subdued economic targets of a breeding bull semen collection

\end{document}

I'd like text to start indented in next line in \paragraph, reduction of vertical space between \section and text start.

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  • the heading level hierarchy is \chapter,\section, \subsection,\subsubsection, \paragraph But you appear to be omitting \subsusbsection this will lead to weird numbering if you increase secnumdepth. Use \subsubsection rather than \paragraph – David Carlisle 2 days ago
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To have the paragraph title in block style:

\titleformat{\paragraph}[block]
  {\bfseries}
  {\theparagraph}
  {}
  {}

To reduce the vertical space after a section title (here set to 0.5ex):

\titlespacing{\section}{0pt}{2ex}{0.5ex}

To indent the first line after every sectioning command:

\usepackage{indentfirst}

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