Hi,
You can simply use the commandbutton for each Contact record on VF page and pass the contact id by using apex:param tag so that in controller you will get that value.
////////////////////////// VF Page ////////////////////////////
<apex:page controller="relatedCon" id="p1">
<apex:form >
<apex:outputPanel id="Panel1">

<apex:repeat value="{!ConDetail}" var="c" >
<apex:inlineEditSupport showOnEdit="Update"
hideOnEdit="editButton" event="ondblclick"
changedStyleClass="myBoldClass" resetFunction="resetInlineEdit"/>
<!-- <apex:pageBlock >
<apex:pageBlockButtons >
<apex:commandButton action="{!edit}" id="editButton" value="Edit"/>
<apex:commandButton action="{!Update1}" id="saveButton" value="Save" reRender="opanel1">
<apex:param name="ConId" value="{!c.id}" assignTo="{!ConId}"/></apex:commandbutton>
<apex:commandButton onclick="resetInlineEdit()" id="cancelButton" value="Cancel"/>
</apex:pageBlockButtons>
</apex:pageBlock>-->
<table width="100%" border="0" id="t1">
<tr><td width="25%"><b>Account Name</b></td>
<td width="25%">
<apex:outputField value="{!c.con.accountid}"/>
<!--<apex:inlineEditSupport showOnEdit="Update"
hideOnEdit="editButton" event="ondblclick"
changedStyleClass="myBoldClass" resetFunction="resetInlineEdit"/></apex:outputField>-->
</td></tr>
<tr><td width="25%"><b>Contact LastName</b></td>
<td width="25%">
<apex:outputField value="{!c.con.lastname}"/>
<!--<apex:inlineEditSupport showOnEdit="Update"
hideOnEdit="editButton" event="ondblclick"
changedStyleClass="myBoldClass" resetFunction="resetInlineEdit"/></apex:outputField>-->
</td></tr>
<tr><td width="25%"><b>Contact ID</b></td>
<td width="25%">
<apex:outputField value="{!c.con.id}"/></td></tr>
</table> <br/>
<center><apex:commandButton value="Update" action="{!Update1}" reRender="p1">
<apex:param name="ConId" value="{!c.con.id}" assignTo="{!ConId}"/>
<apex:param name="IndexId" value="{!c.count}" assignTo="{!IndexId}"/>
</apex:commandButton></center>
<hr/>
</apex:repeat>

</apex:outputPanel>
</apex:form>
</apex:page>
////////////////////////////// Controller //////////////////////////////////
public class relatedCon
{
public list<contact> ConDetail1{get;set;}
public list<wrapCon> ConDetail{get;set;}
public id conId{get;set;}
public integer indexId{get;set;}
public relatedCon()
{
ConDetail=new list<wrapCon>();
ConDetail1=[select id,accountid,lastname from contact where accountid =: ApexPages.currentPage().getParameters().get('id')];
system.debug('@@@@@@@@@@@@@@@@' +ConDetail1.size());
integer count=0;
for(contact w : ConDetail1)
{
ConDetail.add(new wrapCon(w,count));
count++;

}
system.debug('%%%%%%%%%%%%%%%%%%%%%%%' +ConDetail);
}
public void Update1()
{
system.debug('@@@@@@@@-------0th last--------@@@@@@@@@' +ConDetail[0].con.lastname);
system.debug('@@@@@@@@-------1st last--------@@@@@@@@@' +ConDetail[1].con.lastname);
system.debug('@@@@@@@@-------2nd last--------@@@@@@@@@' +ConDetail[2].con.lastname);
system.debug('@@@@@@@@@@@@@@@@@' +conId);
contact con2=new contact(id=conId);
// wrapCon w=new wrapCon(con2);
con2.lastname=ConDetail[indexId].con.lastname;
// system.debug(
con2.accountid=ConDetail[indexId].con.accountid;
update con2;
}
public void edit()
{
}
public class wrapCon
{
public contact con{get;set;}
public integer count{get;set;}
public wrapCon(contact con1,integer count)
{
con=con1;
this.count=count;
}
public wrapCon()
{
}
}
}

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