As we use
<a href="tel:number">number</a> or <a href="mailto:mailid>mailid</a>
for telephone number & email, does anything like <a href="fax:number">number</a>
for fax exist?
Yes, the tel, fax and modem URL Schemes are discussed in https://www.ietf.org/rfc/rfc2806
The URL syntax is formally described as follows (the definition reuses nonterminals from the above definition). For the basis of this syntax, see [RFC2303] and [RFC2304].
fax-url = fax-scheme ":" fax-subscriber
fax-scheme = "fax"
fax-subscriber = fax-global-phone / fax-local-phone
fax-global-phone = "+" base-phone-number [isdn-subaddress]
[t33-subaddress] [post-dial]
*(area-specifier / service-provider /
future-extension)
fax-local-phone = 1*(phonedigit / dtmf-digit /
pause-character) [isdn-subaddress]
[t33-subaddress] [post-dial]
area-specifier
*(area-specifier / service-provider /
future-extension)
t33-subaddress = ";tsub=" 1*phonedigit
The fax: URL is very similar to the tel: URL. The main difference is that in addition to ISDN subaddresses, telefaxes also have an another type of subaddress, see section 2.5.8.
<a href="fax:+358.555.1234567">+358.555.1234567</a>
However, as per the comments below, RFC 2806 was obsoleted by RFC 3966 and you should just use the tel URI scheme:
The "tel" URI does not specify the call type, such as voice, fax, or data call, and does not provide the connection parameters for a data call. The type and parameters are assumed to be negotiated either in-band by the telephone device or through a signaling protocol such as SIP. This document obsoletes RFC 2806.
RFC 3966 was updated by RFC 5341 to formalize URI parameters and require them to be registered with IANA. I am including these here for the sake of completeness. They do not contain any additional information on fax devices.