@ Pcon thanks for your help really I appreciate your effort,

Now, I am facing issue for sending attachment from salesforce to JIRA as JIRA may have attachment size 10MB and In Salesforce easily possible for 15MB so when I tried for sending an attachment more then 3MB facing [Apex Heap Size too large] error ,

Please help me on this how I can sent attachment more than 3 MB from salesforce to JIRA.

Code:

@future(callout=true)
    public static void FutureAddAttachment(Id attachId,Id caseAtchParentId)
    {   
        Attachment attach=new Attachment(id=attachId,ParentId=caseAtchParentId);
        //attach.id=attachId;
        AddAttachment(attach);
    }
    
 
 
 public static void AddAttachment(Attachment attch){
        try{
        // get Connection Detail
        UtilClass objUtilClass=new UtilClass();
        UtilClass.ConnectionWrp obj=objUtilClass.getConnectionDetail();
        
         // get Case Detail
        Case CaseRec=new Case();
        CaseRec.Id=attch.ParentId;
        UtilClass.CaseWrapper objCase=objUtilClass.getCaseDetail(CaseRec);
        String jira_host = 'https://host.atlassian.net';
        String issue =UtilClass.getTicketIssueType(CaseRec.Id).Issue_Type__c;
        Attachment attach = [select Name, Body,BodyLength from Attachment where id=:attch.Id limit 1];

        Blob file_body = attach.Body;
        String file_name = attach.Name;
        System.debug('BodyLength'+attach.BodyLength );
        System.debug('heap size is ' + Limits.getHeapSize() + ' out of ' + Limits.getLimitHeapSize());

        
        String auth_header = 'Basic ' + EncodingUtil.base64Encode(Blob.valueOf(obj.strusername + ':' + obj.strpassword));
        //Attachment attach = [select Name, Body from Attachment limit 1];

        String url = UtilClass.CreateJIRAURL+'/' + objCase.JIRAKEY + '/attachments';
        String boundary = '----------------------------741e90d31eff';
        String header = '--' + boundary + '\n' +
        'Content-Disposition: form-data; name="file"; filename="' + file_name + '";\n' +
        'Content-Type: application/octet-stream';

        String footer = '--' + boundary + '--';
        String headerEncoded = EncodingUtil.base64Encode(Blob.valueOf(header + '\r\n\r\n'));
        while (headerEncoded.endsWith('=')){
        header += ' ';
        headerEncoded = EncodingUtil.base64Encode(Blob.valueOf(header+'\r\n\r\n'));
        }

        String bodyEncoded = EncodingUtil.base64Encode(file_body);

        Blob bodyBlob = null;
        String last4Bytes = bodyEncoded.substring(bodyEncoded.length()-4,bodyEncoded.length());

        if (last4Bytes.endsWith('==')) {
        last4Bytes = last4Bytes.substring(0, 2) + '0K';
        bodyEncoded = bodyEncoded.substring(0, bodyEncoded.length() - 4) + last4Bytes;

        String footerEncoded = EncodingUtil.base64Encode(Blob.valueOf(footer));
        bodyBlob = EncodingUtil.base64Decode(headerEncoded + bodyEncoded + footerEncoded);
        } else if (last4Bytes.endsWith('=')) {
        last4Bytes = last4Bytes.substring(0, 3) + 'N';
        bodyEncoded = bodyEncoded.substring(0, bodyEncoded.length()-4) + last4Bytes;
        footer = '\n' + footer;
        String footerEncoded = EncodingUtil.base64Encode(Blob.valueOf(footer));
        bodyBlob = EncodingUtil.base64Decode(headerEncoded + bodyEncoded + footerEncoded);              
        } else {
        footer = '\r\n' + footer;
        String footerEncoded = EncodingUtil.base64Encode(Blob.valueOf(footer));
        bodyBlob = EncodingUtil.base64Decode(headerEncoded + bodyEncoded + footerEncoded);  
        }

        HttpRequest req = new HttpRequest();
        req.setHeader('Content-Type', 'multipart/form-data; boundary=' + boundary);
        req.setHeader('Authorization', auth_header);
        req.setHeader('X-Atlassian-Token', 'nocheck');
        req.setMethod('POST');
        req.setEndpoint(url);
        req.setBodyAsBlob(bodyBlob);
        req.setTimeout(120000);

        Http h = new Http();
        HTTPResponse res = h.send(req);
        System.debug(res);
        }catch(Exception ex)
        {
        
            System.debug('Exception'+ex);
        }
    }

Its working fine for till 2MB file but if attachment size more then 2.5 MB facing that issue [Apex Heap Size is too large].

@Pcon once again I hope for your help on this.