I need to export history version of sharepoint ( bug posts ). To access SP I need to type credentials. 

When you run your script and you've sufficient permissions (for example you're a member of the farm administrator group) you must not login under different credentials.

But what Log do you want to export? Necessarily you don't need a connection with SP (on the file basis). 

I need to download from SP history of ech topic ( bug ) created by our users. 

Hi Dblade99,

If you want to remote access Sharepoint server in powershell, please follow this aritcle:

Configure Remote PowerShell in SharePoint 2010

#Setup your Remote Server
Enable-PSRemoting -Force
Enable-WSmanCredSSP -Role Server

#Setup your Client Computer 
##GPO:
##Allow Delegating Fresh Credentials 
##Allow Delegating Fresh Credentials with NTLM-only Server Authentication 
Enable-PSRemoting -Force
Enable-WSManCredSSP -Role Client DelegateComputer NameOfServer
#Create and enter a remote session of Windows PowerShell 
Read-Host -AsSecureString | ConvertFrom-SecureString | out-file C:\crd-sharepoint.txt
$pwd = Get-Content C:\crd-sharepoint.txt | ConvertTo-SecureString
$crd = New-Object -TypeName System.Management.Automation.PSCredential -ArgumentList "domain\username",$pwd

$session = New-PSSession -computername "SPServer" -Authentication CredSSP -Credential $crd
Invoke-Command -Session $session -ScriptBlock{Add-PsSnapin Microsoft.SharePoint.PowerShell}

T oexport version history of SharePoint list items in powershell, please refer to this script:

https://gallery.technet.microsoft.com/office/Test-bb3ed1ca

I also recommend you can post your current script and the issue.

If there is anything else regarding this issue, please feel free to post back.

Best Regards,

Anna Wang

I have access only as a normal user. 

Hi Dblade99,

If you want to remote manage sharepoint server, the user account need to have enough permission on the remote server to create pssession.

Best Regards,

Anna