documentclass{amsbook}
usepackage{verbatim}

begin{document}

tableofcontents

chapter[Title with two footnotes]%
  {Titleexcept{toc}{protectfootnote{The first footnote}}
  with two footnotesexcept{toc}{protectfootnote{The second footnote}}}

There is some text in this chapter.footnote{With a footnote}

Footnotes should be avoided on chapter titles whenever possible.
However, if a footnote---or other material that should not go
into the table of contents, such as a line break---is present, the
command verb+except{toc}{...}+ should be wrapped around that element
to suppress it from the contents.

If the header with such a modification may be used in a running head,
either the verb+[...]+ option or a suitable verb+mark...+ command
must be given to omit the modification from the running head.

newpage

There is a second page in this chapter.

chapter*{A starred titleexcept{toc}{protectfootnotemark} with two
  footnotesexcept{toc}{protectfootnotemark}}
markboth{TITLE WITHOUT EITHER FOOTNOTE}{TITLE WITHOUT EITHER FOOTNOTE}

addtocounter{footnote}{-1}
footnotetext{This is the first footnote}
addtocounter{footnote}{1}
footnotetext{This is the second footnote}

Notice that footnote numbering isn't reset for ``starred'' chapters.
Also, the bracketed verb+[...]+ option doesn't work to provide alternate
titles for such chapters so a verb+mark...+ must be used
(this may be changed in the future).
Furthermore, a verb+footnotemark+, although enclosed in braces as an
argument of verb+except+, will gobble the next space, so an explicit
space must be provided.

Section headings can also have footnotesfootnote{An irrelevant footnote}
excluded from the TOC.

section[A section heading with a footnote]%
  {A section heading, with a
  footnote,except{toc}{protectfootnote{And yet another.}}
  that is very longexcept{toc}{protect\}
  so that it hasfor{toc}{protect\} to be broken under input control}

There is also a command verb+for+ that can be used to emph{include}
selected material in the TOC, such as an explicit linebreak different
from one used in the body.

newpage

There is a second page in this chapter.

chapter[Another chapter title]{Another chapter title with a
  footnoteexcept{toc}{protectfootnote{This is another footnote}}}

Footnote numbering emph{is} reset for numbered chapters.

newpage

There is also a second page in this chapter too.

vspace{3baselineskip}
small
verbatiminput{jobname.tex}
end{document}

documentclass{article}

makeatletter
defmyfnt{ifxprotect@typeset@protectexpandafterfootnoteelseexpandafter@gobblefi}
makeatother

begin{document}

tableofcontents

section{AAAmyfnt{this}}
z
section{BBBmyfnt{that}}
z
section{CCCmyfnt{the other}}
z

end{document}

%%PREAMBLE

usepackage[stable]{footmisc}

%%BODY

section{Your Title textsuperscript{footnotesize{footnote{Your foonote}}}}