Can gatsby static query using filter?

StaticQuery has it's own limitations (that's why it's are called static) and they do not allow any dynamic parameter. As it shows Gatsby documention:

How StaticQuery differs from page query

StaticQuery can do most of the things that page query can, including fragments. The main differences are:

• page queries can accept variables (via pageContext) but can only be added to page components
• StaticQuery does not accept variables (hence the name “static”), but can be used in any component, including pages
• StaticQuery does not work with raw React.createElement calls; please use JSX, e.g.

Of course, you can filter using a hardcoded value, this is actually the only solution available for you can't filter using a dynamic value.

Check your localhost:8000/___graphql playground to see if your query works (it should). Usually chained values in GraphQL must be filtered using filter: { country__code: { eq:"CA" }}

Ideally, your useStaticQuery hook file should look like:

import { graphql, useStaticQuery } from 'gatsby';

export const useYourItems = () => {
  const yourItems  = useStaticQuery(
    graphql`
        query MyQuery {
            allStrapiAvailableLanguageByMarkets(filter: {country: {code: {eq: "CA"}}}) {
                nodes {
                    country {
                        code
                    }
                    languages {
                        code
                        name
                    }
                }
            }
        }`,
  );

  return yourItems.allStrapiAvailableLanguageByMarkets;
};

Then, in another component:

  const yourItems = useYourItems();