There is a plugin by Adaptavist, the Advanced Search plugin, which will allow you to search the content of just one page, you can check it out here: https://marketplace.atlassian.com/plugins/com.adaptavist.confluence.advancedSearch
Howeevr, you may find that the content on the page isn't searchable because it is contained in a macro and hasn't been indexed. In this case then you would also want to install the Macro Indexer plugin to ensure that the required content is available to the search index: https://marketplace.atlassian.com/plugins/com.atlassian.confluence.plugins.confluence-macro-indexer-plugin
All the best,
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