var o = {
  '2022-03-12':{name:'abc', age:'abc'},
  '2022-03-08':{name:'cbf', age:'ggg'},
  '2022-03-10':{name:'hhh', age:'chd'},
  '2022-03-20':{name:'jjjj', age:'16'},
  '2022-03-22':{name:'jjjj', age:'16'},
  '2022-03-25':{name:'jjjj', age:'16'},
  '2022-03-30':{name:'jjjj', age:'16'}
}


function xyz(obj, dateX, dateY){
  return Object.keys(obj).reduce((acc,c)=> (+new Date(c) >= +new Date(dateX) && +new Date(c) <= +new Date(dateY)&&(acc[c] = obj[c]), acc ), {})
}


console.log( xyz(o, '2022-03-08', '2022-03-22') )