Spfx webpart to show the list of all webparts

Hi Asesh Kumar Maity 

no, you can't use in classic page.

btw, you can get all spfx webpart in a moder page using this method. 

It require PnP/PnPJs 

  public async GetAllWebpart(): Promise<any[]> {
    // page file
    const file = sp.web.getFileByServerRelativePath(this.context.pageContext.site.serverRequestPath);
    const page = await ClientSidePage.fromFile(file);

    const wpData: any[] = [];

    page.sections.forEach(section => {
      section.columns.forEach(column => {
        column.controls.forEach(control => {
          var wp = { text: control.data.webPartData.title, key: control.data.webPartData.instanceId };
          wpData.push(wp);
        });

      });
    });
    return wpData;
  }

Cheers,

Federico