Hello Dasari,
As i understood about your requirment
i am sending vf page and class i feel this suits your requirement.

VF Page:
<apex:page standardController="case" extensions="caseattachment">
    <apex:form id="frm">
        <apex:pageBlock title="Case Edit">
            <apex:pageBlockSection title="Case Information" collapsible="false">
                <apex:pageBlockSectionItem>
                    <apex:outputLabel value="Case Owner"/>     
                    <apex:outputlabel value="{!$User.FirstName} {!$User.LastName}"/>
                </apex:pageBlockSectionItem>
                    <apex:inputField value="{!objcase.Status}"/>
                    <apex:inputField value="{!objcase.Type}"/>
                    <apex:inputField value="{!objcase.Origin}"/>               
            </apex:pageBlockSection>      
        <apex:pageBlockButtons>
            <apex:commandButton value="Save" action="{!save}"/>
        </apex:pageBlockButtons>       
        <apex:pageBlockSection title="Uploading the Attachment" collapsible="false" dir="LTR" columns="1">
        <div id="upload" class="upload">                                   
            <apex:inputFile id="fileToUpload" value="{!fileBody}" filename="{!fileName}" styleClass="input-file"/>                            
        </div> 
         </apex:pageBlockSection>           
       </apex:pageBlock>        
    </apex:form>
</apex:page>

Apex Class:

public class caseattachment
{
public case objcase{get;set;}
public Attachment myAttachment{get;set;}
public string fileName{get;set;} 
public Blob fileBody{get;set;}

    public caseattachment(Apexpages.standardcontroller controller)
    {
        objcase = new case();
        myAttachment =new Attachment();
    }
    public pagereference save()
    {
        insert objcase;
        System.debug('@@@@@fileBody'+fileBody);     
        myAttachment  = new Attachment();
              Integer i=0;
              myAttachment .clear();
              myAttachment.Body = fileBody; 
              myAttachment.Name = 'Logo_'+objcase.id+'.jpeg' ; 
              myAttachment.ParentId = objcase.id;             
              insert myAttachment;                 
        pagereference pr = new pagereference('/'+objcase.id);                           
        return pr;
    }
}


if you get any doubts in this please feel free to ask me

Hit Kudos if this provides you with useful information and if this is what you where looking for then please mark it as a solution for other benefits.

Thank You,
Srinivas
SFDC Certified Developer