Hi,

You cannot achieve this feature in inbuilt future you have to do customization here i am posting some sample code snippeet please go through it.

S.NoComponent
1)Create New Object
Singular Label: ObjectsExistingFieldsInfo
Plural Label: ObjectsExistingFieldsInfos
Object Name: ObjectsExistingFieldsInfo
Standard Field
Field Label: ObjectsExistingFieldsInfo
Data Type: Auto Number
Display Format: ObjInfo-{000}
2)Create New Field
Object Name: ObjectsExistingFieldsInfo
Field Label: Field API Name
Field Name: Field_API_Name
Data Type: Text (255)
3)Create New Field
Object Name: ObjectsExistingFieldsInfo
Field Label: Fields Count
Field Name: Fields_Count
Data Type: Number (18,0)
4)Create New Field
Object Name: ObjectsExistingFieldsInfo
Field Label: Fields Info
Field Name: Fields_Info
Data Type: Long Text Area

-----------------------------------------------
 

global class FieldsValidator implements Database.Batchable<Sobject> {
    global Database.queryLocator start(Database.BatchableContext bc) {
        return Database.getQueryLocator('select name, fields_info__c, fields_count__c from ObjectsExistingFieldsInfo__c');
    }
    global void execute(Database.BatchableContext bc, List<SObject> sobjLst) {
        String[] types = new String[]{'Account','Contact'};
        String emailBody = '';
        // Make the describe call
        Schema.DescribeSobjectResult[] results = Schema.describeSObjects(types);
        Map<String,List<Field>> objFieldsDesMap = new Map<String,List<Field>>();
        // For each returned result, get some info
        for(Schema.DescribeSobjectResult res : results) {
            Map<String, Schema.SObjectField> objectFields = res.fields.getMap();
            for(Schema.SObjectField fDes : objectFields.values()) {
                if(fDes.getDescribe().isCustom()) {
                    system.debug(fDes.getDescribe().getName()+'@@@'+fDes.getDescribe().getType());
                    String fieldAPIName = String.valueOf(fDes.getDescribe().getName());
                    String fieldDataType = String.valueOf(fDes.getDescribe().getType());
                    if(objFieldsDesMap.containsKey(res.getName())) {
                        objFieldsDesMap.get(res.getName()).add(new Field(fieldAPIName,fieldDataType));
                    }
                    else {
                        objFieldsDesMap.put(res.getName(),new List<Field>{new Field(fieldAPIName,fieldDataType)});
                    }
                }       
            }
        }
        Map<String, ObjectsExistingFieldsInfo__c> objectInfoMap = new Map<String, ObjectsExistingFieldsInfo__c>();
        for(ObjectsExistingFieldsInfo__c objInfo : [select Field_API_Name__c , Fields_Count__c, Fields_Info__c from 
        ObjectsExistingFieldsInfo__c where Field_API_Name__c in: types]) {
            objectInfoMap.put(objInfo.Field_API_Name__c,objInfo);
        }
        for(String type : types) {
            if(objectInfoMap.get(type).fields_count__c == null) {
                objectInfoMap.get(type).fields_count__c = objFieldsDesMap.get(type).size();
                objectInfoMap.get(type).fields_info__c = JSON.serialize(objFieldsDesMap.get(type));
            }
            else {
                System.debug('entering to else condition...');
                System.debug('entering to for loop..');
                List<Field> exstingFields = new List<Field>();
                List<Field> newFields = new List<Field>();
                Map<String,Field> bkupexstingFields = new Map<String,Field>();
                Map<String,Field> bkupnewFields = new Map<String,Field>();
                exstingFields = (List<Field>)JSON.deserialize(objectInfoMap.get(type).fields_info__c, List<Field>.class);
                System.debug('exstingFields: '+exstingFields);
                newFields.addAll(objFieldsDesMap.get(type));
                System.debug('objFieldsDesMap: '+objFieldsDesMap);
                System.debug('newFields: '+newFields);
                for(Field f : exstingFields) {
                    bkupexstingFields.put(f.apiName,f);
                }
                for(Field f : newFields) {
                    bkupnewFields.put(f.apiName,f);
                }
                for(Field f : exstingFields) {
                    bkupnewFields.remove(f.apiName);
                }
                for(Field f : newFields) {
                    bkupexstingFields.remove(f.apiName);
                }
                System.debug(bkupnewFields+'@@@'+bkupexstingFields);
                emailBody += type + ' : ';
                //for new fields
                for(Field f :bkupnewFields.values()) {
                    emailBody += f.apiName + ' with datatype '+f.dataType+' is newly created.'; 
                }
                objectInfoMap.get(type).fields_count__c = objFieldsDesMap.get(type).size();
                objectInfoMap.get(type).fields_info__c = JSON.serialize(objFieldsDesMap.get(type));
            }
        }
        /*** Sending Email ***/
        Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();
        mail.setToAddresses(new List<String>{system.label.Dev_Admin});
        mail.setSubject('Fields Update');
        mail.setPlainTextBody(emailBody);
        update objectInfoMap.values();
        Messaging.sendEmail(new Messaging.SingleEmailMessage[]{mail});
    }
    global void finish(Database.BatchableContext bc) {
    } 
    public class Field {
        String apiName, dataType;
        public Field(String apiName, String dataType) {
            this.apiName = apiName;
            this.dataType = dataType;
        }
    }
}

Note:
We cannot create trigger on 'Object' or 'Field'.
Alternative is creating a Batch Class and schedule it as per the requirement.
To store the history of the fields we can user either list custom settings or custom object.
List Custom Settings is not supporting Text Area Long.
To store the history of the fields we need Text Area Long (255 character for text area data type is not sufficient.) field which is possible with the custom object